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///
/// @file nth_prime.cpp
/// @brief Test the nth_prime(n) function for large values of n.
/// For large computations nth_prime(n) uses either
/// pi_legendre(x), pi_meissel(x) or pi_gourdon(x) under the
/// hood. This test has been moved to the test/api directory
/// so that it is executed after the Legendre, Meissel and
/// Gourdon algorithm tests.
///
/// Copyright (C) 2023 Kim Walisch, <kim.walisch@gmail.com>
///
/// This file is distributed under the BSD License. See the COPYING
/// file in the top level directory.
///
#include <primecount.hpp>
#include <primesieve.hpp>
#include <PiTable.hpp>
#include <stdint.h>
#include <iostream>
#include <cstdlib>
#include <random>
using namespace primecount;
void check_equal(int64_t n,
int64_t res1,
int64_t res2)
{
bool OK = (res1 == res2);
std::cout << "nth_prime(" << n << ") = " << res1 << " " << (OK ? "OK" : "ERROR") << "\n";
if (!OK)
std::exit(1);
}
int main()
{
primesieve::iterator iter(PiTable::max_cached() + 1);
int64_t n = PiTable::pi_cache(PiTable::max_cached()) + 1;
int64_t limit_small = n + 100;
int64_t prime = iter.next_prime();
// Test first few n > pi(PiTable::max_cached())
for (; n < limit_small; n++)
{
check_equal(n, nth_prime(n), prime);
prime = iter.next_prime();
}
std::random_device rd;
std::mt19937 gen(rd());
std::uniform_int_distribution<int64_t> dist(1, 10000);
// Test random increment, goes up to ~ 5*10^6
for (int64_t i = 0; i < 1000; i++)
{
int64_t next_n = n + dist(gen);
for (; n < next_n; n++)
prime = iter.next_prime();
check_equal(n, nth_prime(n), prime);
}
// nth_prime(1e7)
n = 10000000ll;
check_equal(n, nth_prime(n), 179424673ll);
// nth_prime(1e8)
n = 100000000ll;
check_equal(n, nth_prime(n), 2038074743ll);
// nth_prime(1e9)
n = 1000000000ll;
check_equal(n, nth_prime(n), 22801763489ll);
// nth_prime(1e10)
n = 10000000000ll;
check_equal(n, nth_prime(n), 252097800623ll);
// nth_prime(1e11)
n = 100000000000ll;
check_equal(n, nth_prime(n), 2760727302517ll);
// nth_prime(1e12)
n = 1000000000000ll;
check_equal(n, nth_prime(n), 29996224275833ll);
// nth_prime(1e13)
n = 10000000000000ll;
check_equal(n, nth_prime(n), 323780508946331ll);
std::cout << std::endl;
std::cout << "All tests passed successfully!" << std::endl;
return 0;
}
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