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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);

Maybe you'll have better luck with that.

Some properties:

  • It only keeps m+1 Ackermann numbers in memory at once.
  • It never calculates the same Ackermann number twice.

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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