Ackermann function

The Ackermann function is a classic recursive example in computer science. It is a function that grows very quickly (in its value and in the size of its call tree). It is defined as follows:

Ackermann function
You are encouraged to solve this task according to the task description, using any language you may know.

          n+1               if m=0
A(m, n) = A(m-1, 1)         if m>0 and n=0
          A(m-1, A(m,n-1))  if m>0 and n>0

Its arguments are never negative and it always terminates. Write a function which returns the value of A(m, n). Arbitrary precision is preferred (since the funciton grows so quickly), but not required.

Java

<java>public static BigInteger ack(BigInteger m, BigInteger n){ if(m.equals(BigInteger.ZERO)) return n.add(BigInteger.ONE);

if(m.compareTo(BigInteger.ZERO) > 0 && n.equals(BigInteger.ZERO)) return ack(m.subtract(BigInteger.ONE), BigInteger.ONE);

if(m.compareTo(BigInteger.ZERO) > 0 && n.compareTo(BigInteger.ZERO) > 0) return ack(m.subtract(BigInteger.ONE), ack(m, n.subtract(BigInteger.ONE)));

return null; }</java>