Ackermann function computed with stack simulation

ackermann_stack.c

/*
 *  Copyright (c) 2020 by Reto Kromer
 *
 *  Ackermann function:
 *
 *    A(0,n) = n+1
 *    A(m,0) = A(m-1,1)         if m > 0
 *    A(m,n) = A(m-1,A(m,n-1))  if m > 0 and n > 0
 *
 *    where m and n are non-negative integers
 *
 *   computed with stack simulation.
 * 
 *  This C program is released under a 3-Clause BSD License and is provided
 *  "as is" without warranty or support of any kind.
 */

#include <stdio.h>
#include <stdlib.h>


int A(unsigned int m, unsigned int n) {
  unsigned int s = 0, *M;
  M = (unsigned int *)malloc(sizeof(unsigned int));
  if (M == NULL) {
    fprintf(stderr, "Error: malloc failed.\n");
    exit(1);
  }

  for (;;) {
    if (m == 0) {
      if (s == 0) {
        return ++n;
      } else {
        n++;
        m = M[s--] - 1;
      }
    } else if (n == 0) {
      m--;
      n = 1;
    } else {
      M[++s] = m;
      n--;
    }
  }

  free(M);
  return n;
}


int main(int argc, char* argv[]) {
  unsigned int m, n;

  if (argc == 3) {
    m = atoi(argv[1]);
    n = atoi(argv[2]);
  } else {
    printf("%s", "m = ");
    scanf("%d", &m);
    printf("%s", "n = ");
    scanf("%d", &n);
  }

  printf("A(%d,%d) = %d\n", m, n, A(m,n));

  return 0;
}