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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

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