## Seive of Atkin

What can be done to enhance this code. Like its gotta be bug free and efficient enough

Code:
```#include <iostream>
#include <cmath>
#include <fstream>
using namespace std;
int main (int argc, char* argv[])
{
//Create the various different variables required
int limit = 1000000;
int root = ceil(sqrt(limit));
bool sieve[limit];
int primes[(limit/2)+1];
int insert = 2;
primes[0] = 2;
primes[1] = 3;
for (int z = 0; z < limit; z++) sieve[z] = false; //Not all compilers have false as the default boolean value
for (int x = 1; x <= root; x++)
{
for (int y = 1; y <= root; y++)
{
//Main part of Sieve of Atkin
int n = (4*x*x)+(y*y);
if (n <= limit && (n % 12 == 1 || n % 12 == 5)) sieve[n] ^= true;
n = (3*x*x)+(y*y);
if (n <= limit && n % 12 == 7) sieve[n] ^= true;
n = (3*x*x)-(y*y);
if (x > y && n <= limit && n % 12 == 11) sieve[n] ^= true;
}
}
//Mark all multiples of squares as non-prime
for (int r = 5; r <= root; r++) if (sieve[r]) for (int i = r*r; i < limit; i += r*r) sieve[i] = false;
for (int a = 5; a < limit; a++)
{
if (sieve[a])
{
primes[insert] = a;
insert++;
}
}
//The following code just writes the array to a file
ofstream file;
char filename[100];
sprintf(filename, "primes_%d.txt", limit);
file.open(filename);
for (int a = 0; a < insert; a++) file << primes[a] << ((a == insert-1) ? "" : "\n");
file.close();
cout << "Written to file.\n";
return 0;
}```