order_n.c

uint64_t o1_add(const uint64_t a, const uint64_t b); /* Implemented */
uint64_t o2_mul(const uint64_t a, const uint64_t b); /* Implemented */
uint64_t o3_exp(const uint64_t a, const uint64_t b); /* Implemented */
uint64_t o4_tet(const uint64_t a, const uint64_t b); /* Implemented */
uint64_t order_n(const uint64_t n, const uint64_t a, const uint64_t b);

uint64_t o1_add(const uint64_t a, const uint64_t b)
{
  uint64_t res;

  res = a;
  for (uint64_t i=0; i<b; ++i)
    ++res;
  return (res);
}

uint64_t o2_mul(const uint64_t a, const uint64_t b)
{
  uint64_t res;

  res = 0;
  for (uint64_t i=0; i<b; ++i)
    res = o1_add(res, a);
  return (res);
}

uint64_t o3_exp(const uint64_t a, const uint64_t b)
{
  uint64_t res;

  res = 1;
  for (uint64_t i=0; i<b; ++i)
    res = o2_mul(res, a);
  return (res);
}

uint64_t o4_tet(const uint64_t a, const uint64_t b)
{
  uint64_t res;

  res = a;
  for (uint64_t i=0; i<b; ++i)
    res = o3_exp(res, a);
  return (res);
}

uint64_t order_n(const uint64_t n, const uint64_t a, const uint64_t b)
{
  uint64_t res;

  if (n <= 1)
    return (a+b);
  res = 0;
  for (uint64_t i=0; i<b; ++i)
    res = order_n(n-1, res, a);
  return (res);
}

int main(void)
{
  printf("2*60 = %Ld\n", o2_mul(2, 60));
  printf("24*4 = %Ld\n", o2_mul(24, 4));
  printf("10*0 = %Ld\n", o2_mul(10, 0));
  printf("2^10 = %Ld\n", o3_exp(2, 10));
  printf("2^^4 = %Ld\n", o4_tet(2, 4));
  putchar('\n');

  printf("O(1, 10, 4) = %Ld\n", order_n(1, 10, 4));
  printf("O(2, 10, 4) = %Ld\n", order_n(2, 10, 4));
  printf("O(3, 10, 4) = %Ld", order_n(3, 10, 4));

  return (EXIT_SUCCESS);
}