#include "nth_prime.h"

#include <cmath>
#include <cstring>
#include <stdexcept>
#include <vector>


namespace prime {

using namespace std;

number_t nth(size_t n, size_t sieve_size)
{
    if (n < 1)
        throw domain_error("invalid prime number index");

    if (n == 1)
        return 2;

    vector<number_t> primes = {3, 5, 7, 11, 13};

    if (n - 2 < primes.size())
        return primes[n - 2];

    primes.reserve(n - 1);

    if (auto_sieve_size == sieve_size) {

        sieve_size = min(size_t(32 * 1024),
                         size_t(0.5*(n * (log(n) + log(log(n)))) + 0.5));
    }

    vector<char> sieve(sieve_size, false);

    sieve[0] = true;

    size_t first_number = 1;

    while (true) {

        for (auto p : primes) {

            size_t reminder = (first_number % (2*p));
            size_t begin    = reminder > p ? 3*p - reminder : p - reminder;

            begin /= 2;

            for (size_t i = begin; i < sieve_size; i += p) {

                sieve[i] = true;
            }
        }

        for (size_t i = 0; i < sieve_size; ++i) {

            if (sieve[i])
                continue;

            number_t p = first_number + 2*i;
            primes.push_back(p);

            if (primes.size() == n - 1)
                return p;

            for (size_t j = i; j < sieve_size; j += p) {

                sieve[j] = true;
            }
        }

        size_t next_first_number = first_number + 2*sieve_size;

        if (next_first_number < first_number)
            throw runtime_error("failed to reach prime number");

        first_number = next_first_number;
        memset(&sieve[0], false, sieve.size()*sizeof(sieve[0]));
    }
}

}