How to resolve the algorithm Ackermann function step by step in the X86 Assembly programming language

Published on 12 May 2024 09:40 PM
#X86 assembly

How to resolve the algorithm Ackermann function step by step in the X86 Assembly 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 X86 Assembly programming language

Source code in the x86 programming language

section .text

global _main
_main:
    mov eax, 3 ;m
    mov ebx, 4 ;n
    call ack ;returns number in ebx
    ret
    
ack:
    cmp eax, 0
    je M0 ;if M == 0
    cmp ebx, 0
    je N0 ;if N == 0
    dec ebx ;else N-1
    push eax ;save M
    call ack1 ;ack(m,n) -> returned in ebx so no further instructions needed
    pop eax ;restore M
    dec eax ;M - 1
    call ack1 ;return ack(m-1,ack(m,n-1))
    ret
    M0:
        inc ebx ;return n + 1
        ret
    N0:
        dec eax
        inc ebx ;ebx always 0: inc -> ebx = 1
        call ack1 ;return ack(M-1,1)
        ret

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