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sascomputation-theory

Writing the Ackermann function in a SAS data step

In my quest to understand recursive programming in SAS, I have tried, unsuccessfully many times, to write a version of a two-argument Ackermann function.

The function states that:

I was only going to calculate m & n for values ranging from 0 - 3, as values of m >= 4 cause the returned values to become large very rapidly.

I was shooting for a relatively simple output; something like:

Ack(0,0) = 1
Ack(0,1) = 2
Ack(0,2) = 3
Ack(0,3) = 4
Ack(1,0) = 2
Ack(1,1) = 3

And so on to Ack(3,3) = 61

I was unable to find any reference online to someone doing this in SAS. So, if someone could help me with this, I would really appreciate it!

Thanks!

Solution

  • It is difficult to do recursion in normal SAS code. But it is easy in macro code.

    %macro a(m,n);
%if %sysfunc(verify(&m.&n,0123456789)) %then %do;
  %put WARNING: Invalid input to macro &sysmacroname.. Use only non-negative integers.;
  .
%end;
%else %if (&m=0) %then %eval(&n+1);
%else %if (&n=0) %then %a(%eval(&m-1),1);
%else %a(%eval(&m-1),%a(&m,%eval(&n-1)));
%mend a;

    If you must use it with the values of dataset variables then you might consider using the resolve() function.

    data testa;
  do i=0 to 3; do j=0 to 3;
    a=input(resolve(cats('%a(',i,',',j,')')),32.);
    output;
  end;end;
run;
proc print; run;

    Results

    Obs    i    j     a

  1    0    0     1
  2    0    1     2
  3    0    2     3
  4    0    3     4
  5    1    0     2
  6    1    1     3
  7    1    2     4
  8    1    3     5
  9    2    0     3
 10    2    1     5
 11    2    2     7
 12    2    3     9
 13    3    0     5
 14    3    1    13
 15    3    2    29
 16    3    3    61

    Of course if you are only ever going to use arguments from 0 to 3 then perhaps you just need to use an array lookup instead.

    data testb;
  array _a(0:3,0:3) _temporary_
(1 2 3 4
 2 3 4 5
 3 5 7 9
 5 13 29 61
);
 do i=0 to 3; do j=0 to 3; a=_a(i,j); output; end; end;
run;