How to resolve the algorithm Ackermann function step by step in the Forth programming language

Published on 12 May 2024 09:40 PM
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How to resolve the algorithm Ackermann function step by step in the Forth programming language

Table of Contents

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:

Step by Step solution about How to resolve the algorithm Ackermann function step by step in the Forth programming language

Source code in the forth programming language

: acker ( m n -- u )
	over 0= IF  nip 1+ EXIT  THEN
	swap 1- swap ( m-1 n -- )
	dup  0= IF  1+  recurse EXIT  THEN
	1- over 1+ swap recurse recurse ;


: ackermann                            ( m n -- u ) 
  over                                 ( case statement) 
  0 over = if drop nip 1+     else
  1 over = if drop nip 2 +    else
  2 over = if drop nip 2* 3 + else
  3 over = if drop swap 5 + swap lshift 3 - else
    drop swap 1- swap dup
    if
      1- over 1+ swap recurse recurse exit
    else
      1+ recurse exit                  \ allow tail recursion
    then
  then then then then
;

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