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///
/// @file Ri.cpp
/// @brief Test the Riemann R function.
///
/// Copyright (C) 2021 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-internal.hpp>
#include <imath.hpp>
#include <stdint.h>
#include <iostream>
#include <cstdlib>
#include <vector>
using std::max;
using std::size_t;
using namespace primecount;
std::vector<int64_t> Ri_table =
{
4, // Ri(10^1)
25, // Ri(10^2)
168, // Ri(10^3)
1226, // Ri(10^4)
9587, // Ri(10^5)
78527, // Ri(10^6)
664667, // Ri(10^7)
5761551, // Ri(10^8)
50847455, // Ri(10^9)
455050683, // Ri(10^10)
4118052494ll, // Ri(10^11)
37607910542ll, // Ri(10^12)
346065531065ll, // Ri(10^13)
3204941731601ll // Ri(10^14)
};
void check(bool OK)
{
std::cout << " " << (OK ? "OK" : "ERROR") << "\n";
if (!OK)
std::exit(1);
}
int main()
{
for (size_t i = 0; i < Ri_table.size(); i++)
{
int p = (int) i + 1;
int64_t x = ipow(10ll, p);
std::cout << "Ri(" << x << ") = " << Ri(x);
check(Ri(x) == Ri_table[i]);
}
for (size_t i = 0; i < Ri_table.size(); i++)
{
int p = (int) i + 1;
int64_t x = ipow(10ll, p);
std::cout << "Ri_inverse(" << Ri_table[i] << ") = " << Ri_inverse(Ri_table[i]);
check(Ri_inverse(Ri_table[i]) < x &&
Ri_inverse(Ri_table[i] + 1) >= x);
}
int64_t x;
// Sanity checks for tiny values of Ri(x)
for (x = 0; x < 10000; x++)
{
int64_t rix = Ri(x);
double logx = std::log(max((double) x, 2.0));
if (rix < 0 ||
(x >= 20 && rix < x / logx) ||
(x >= 2 && rix > x * logx))
{
std::cout << "Ri(" << x << ") = " << rix << " ERROR" << std::endl;
std::exit(1);
}
}
// Sanity checks for small values of Ri(x)
for (; x < 100000; x += 101)
{
int64_t rix = Ri(x);
double logx = std::log(max((double) x, 2.0));
if (rix < 0 ||
(x >= 20 && rix < x / logx) ||
(x >= 2 && rix > x * logx))
{
std::cout << "Ri(" << x << ") = " << rix << " ERROR" << std::endl;
std::exit(1);
}
}
// Sanity checks for tiny values of Ri_inverse(x)
for (x = 2; x < 1000; x++)
{
int64_t res = Ri_inverse(x);
double logx = std::log((double) x);
if (res < 0 ||
res < x ||
(x >= 5 && res > x * logx * logx))
{
std::cout << "Ri_inverse(" << x << ") = " << res << " ERROR" << std::endl;
std::exit(1);
}
}
// Sanity checks for small values of Ri_inverse(x)
for (; x < 100000; x += 101)
{
int64_t res = Ri_inverse(x);
double logx = std::log((double) x);
if (res < 0 ||
res < x ||
(x >= 5 && res > x * logx * logx))
{
std::cout << "Ri_inverse(" << x << ") = " << res << " ERROR" << std::endl;
std::exit(1);
}
}
std::cout << std::endl;
std::cout << "All tests passed successfully!" << std::endl;
return 0;
}
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