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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,138 @@ | ||
| /// | ||
| /// @file Riemann_R.cpp | ||
| /// @brief Test the Riemann R function. | ||
| /// | ||
| /// Copyright (C) 2024 Kim Walisch, <[email protected]> | ||
| /// | ||
| /// This file is distributed under the BSD License. See the COPYING | ||
| /// file in the top level directory. | ||
| /// | ||
|
|
||
| #include <primesieve/nthPrimeApprox.hpp> | ||
|
|
||
| #include <stdint.h> | ||
| #include <iostream> | ||
| #include <cstdlib> | ||
| #include <cmath> | ||
| #include <limits> | ||
| #include <vector> | ||
|
|
||
| using std::max; | ||
| using std::size_t; | ||
| using namespace primesieve; | ||
|
|
||
| std::vector<uint64_t> RiemannR_table = | ||
| { | ||
| 4, // RiemannR(10^1) | ||
| 25, // RiemannR(10^2) | ||
| 168, // RiemannR(10^3) | ||
| 1226, // RiemannR(10^4) | ||
| 9587, // RiemannR(10^5) | ||
| 78527, // RiemannR(10^6) | ||
| 664667, // RiemannR(10^7) | ||
| 5761551, // RiemannR(10^8) | ||
| 50847455, // RiemannR(10^9) | ||
| 455050683, // RiemannR(10^10) | ||
| 4118052494ll, // RiemannR(10^11) | ||
| 37607910542ll, // RiemannR(10^12) | ||
| 346065531065ll, // RiemannR(10^13) | ||
| 3204941731601ll // RiemannR(10^14) | ||
| }; | ||
|
|
||
| void check(bool OK) | ||
| { | ||
| std::cout << " " << (OK ? "OK" : "ERROR") << "\n"; | ||
| if (!OK) | ||
| std::exit(1); | ||
| } | ||
|
|
||
| int main() | ||
| { | ||
| uint64_t x = 1; | ||
| for (size_t i = 0; i < RiemannR_table.size(); i++) | ||
| { | ||
| x *= 10; | ||
| std::cout << "RiemannR(" << x << ") = " << RiemannR(x); | ||
| check(RiemannR(x) == RiemannR_table[i]); | ||
| } | ||
|
|
||
| x = 1; | ||
| for (size_t i = 0; i < RiemannR_table.size(); i++) | ||
| { | ||
| x *= 10; | ||
| std::cout << "RiemannR_inverse(" << RiemannR_table[i] << ") = " << RiemannR_inverse(RiemannR_table[i]); | ||
| check(RiemannR_inverse(RiemannR_table[i]) < x && | ||
| RiemannR_inverse(RiemannR_table[i] + 1) >= x); | ||
| } | ||
|
|
||
| // Sanity checks for tiny values of RiemannR(x) | ||
| for (x = 0; x < 10000; x++) | ||
| { | ||
| uint64_t rix = RiemannR(x); | ||
| double logx = std::log(max((double) x, 2.0)); | ||
|
|
||
| if ((x >= 20 && rix < x / logx) || | ||
| (x >= 2 && rix > x * logx)) | ||
| { | ||
| std::cout << "RiemannR(" << x << ") = " << rix << " ERROR" << std::endl; | ||
| std::exit(1); | ||
| } | ||
| } | ||
|
|
||
| // Sanity checks for small values of RiemannR(x) | ||
| for (; x < 100000; x += 101) | ||
| { | ||
| uint64_t rix = RiemannR(x); | ||
| double logx = std::log(max((double) x, 2.0)); | ||
|
|
||
| if ((x >= 20 && rix < x / logx) || | ||
| (x >= 2 && rix > x * logx)) | ||
| { | ||
| std::cout << "RiemannR(" << x << ") = " << rix << " ERROR" << std::endl; | ||
| std::exit(1); | ||
| } | ||
| } | ||
|
|
||
| // Sanity checks for tiny values of RiemannR_inverse(x) | ||
| for (x = 2; x < 1000; x++) | ||
| { | ||
| uint64_t res = RiemannR_inverse(x); | ||
| double logx = std::log((double) x); | ||
|
|
||
| if (res < x || | ||
| (x >= 5 && res > x * logx * logx)) | ||
| { | ||
| std::cout << "RiemannR_inverse(" << x << ") = " << res << " ERROR" << std::endl; | ||
| std::exit(1); | ||
| } | ||
| } | ||
|
|
||
| // Sanity checks for small values of RiemannR_inverse(x) | ||
| for (; x < 100000; x += 101) | ||
| { | ||
| uint64_t res = RiemannR_inverse(x); | ||
| double logx = std::log((double) x); | ||
|
|
||
| if (res < x || | ||
| (x >= 5 && res > x * logx * logx)) | ||
| { | ||
| std::cout << "RiemannR_inverse(" << x << ") = " << res << " ERROR" << std::endl; | ||
| std::exit(1); | ||
| } | ||
| } | ||
|
|
||
| { | ||
| uint64_t x = std::numeric_limits<uint64_t>::max() / 10; | ||
| uint64_t res = RiemannR_inverse(x); | ||
| if (res != std::numeric_limits<uint64_t>::max()) | ||
| { | ||
| std::cout << "RiemannR_inverse(" << x << ") != UINT64_MAX, failed to prevent integer overflow!" << std::endl; | ||
| std::exit(1); | ||
| } | ||
| } | ||
|
|
||
| std::cout << std::endl; | ||
| std::cout << "All tests passed successfully!" << std::endl; | ||
|
|
||
| return 0; | ||
| } |