Problem Statement

The Ackermann function is a classic example of a recursive function, notable especially because it is not a primitive recursive function. It grows very quickly in value, as does the size of its call tree.

The Ackermann function is usually defined as follows:

Its arguments are never negative and it always terminates.

Write a function which returns the value of

A ( m , n )

{\displaystyle A(m,n)}

. Arbitrary precision is preferred (since the function grows so quickly), but not required.

Let's start with the solution:

A(m, n) {
  If (m > 0) && (n = 0)
    Return A(m-1,1)
  Else If (m > 0) && (n > 0)
    Return A(m-1,A(m, n-1))
  Else If (m=0)
    Return n+1
}

; Example:
MsgBox, % "A(1,2) = " A(1,2)