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///
/// @file P2.cpp
/// @brief Test the 2nd partial sieve function P2(x, a)
/// that counts the numbers <= x that have exactly
/// 2 prime factors each exceeding the a-th prime.
///
/// 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 <primecount-internal.hpp>
#include <generate_primes.hpp>
#include <imath.hpp>
#include <stdint.h>
#include <iostream>
#include <cstdlib>
#include <vector>
#include <random>
using std::size_t;
using namespace primecount;
void check(bool OK)
{
std::cout << " " << (OK ? "OK" : "ERROR") << "\n";
if (!OK)
std::exit(1);
}
int main()
{
// Test small x values
{
std::random_device rd;
std::mt19937 gen(rd());
std::uniform_int_distribution<int> dist(2, 1000);
for (int i = 0; i < 100; i++)
{
int threads = 1;
int64_t x = dist(gen);
auto primes = generate_primes<int64_t>(x);
for (int a = 1; primes[a] <= isqrt(x); a++)
{
int64_t p2 = 0;
for (size_t b = a + 1; b < primes.size(); b++)
{
for (size_t c = b; c < primes.size(); c++)
{
if (primes[b] * primes[c] <= x)
p2++;
else
break;
}
}
std::cout << "P2(" << x << ", " << a << ") = " << p2;
check(p2 == P2(x, primes[a], a, threads));
}
}
}
// Test medium x values
{
std::random_device rd;
std::mt19937 gen(rd());
std::uniform_int_distribution<int> dist(1000, 200000);
for (int i = 0; i < 100; i++)
{
int threads = 1;
int64_t x = dist(gen);
auto primes = generate_primes<int64_t>(x);
for (int a = 1; primes[a] <= isqrt(x); a++)
{
int64_t p2 = 0;
for (size_t b = a + 1; b < primes.size(); b++)
{
for (size_t c = b; c < primes.size(); c++)
{
if (primes[b] * primes[c] <= x)
p2++;
else
break;
}
}
std::cout << "P2(" << x << ", " << a << ") = " << p2;
check(p2 == P2(x, primes[a], a, threads));
}
}
}
int threads = get_num_threads();
{
// Test P2(1e13) and compare with known correct value
int64_t x = 10000000000000ll;
int64_t y = 178815;
int64_t a = 16229;
int64_t res1 = P2(x, y, a, threads);
int64_t res2 = 113111712222ll;
std::cout << "P2(" << x << ", " << y << ", " << a << ") = " << res1;
check(res1 == res2);
}
#ifdef HAVE_INT128_T
{
// Test P2(1e14) and compare with known correct value
int128_t x = 100000000000000ll;
int64_t y = 494134;
int64_t a = 41080;
int128_t res1 = P2(x, y, a, threads);
int128_t res2 = 1026583290763ll;
std::cout << "P2(" << x << ", " << y << ", " << a << ") = " << res1;
check(res1 == res2);
}
#endif
std::cout << std::endl;
std::cout << "All tests passed successfully!" << std::endl;
return 0;
}
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