Using the dependency graph I posted earlier, I was able to construct a non-recursive implementation of the Ackermann function. It visits the graph left to right, top to bottom. 

use strict;
use warnings;
use feature qw( say );

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

   # $A[$m] holds A($m, $n[$m])
   my (@n, @A);

   for my $mi (0..$m) {
      $n[$mi] = -1;
      $A[$mi] = 1;
   }

   for (;;) {
      ++$n[0];
      $A[0] = $n[0] + 1;

      for my $mi (1..$m) {
         last if $A[$mi] != $n[$mi-1];
         $A[$mi] = $A[$mi-1];
         ++$n[$mi];
      }

      return $A[$m] if $n[$m] == $n;
   }
}

say A(@ARGV);

[download]

Maybe you'll have better luck with that.

Some properties:

m<4 can be special-cased. Known formula exist for A(0,n), A(1,n), A(2,n) and A(3,n).

Update: Cleaned up code a bit.

In reply to Re: Non-recursive Ackermann by ikegami
in thread [OT]: threading recursive subroutines. by BrowserUk

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