355 lines
8.6 KiB
C++
355 lines
8.6 KiB
C++
#include "../s2ga.hpp"
|
||
#include <catch2/benchmark/catch_benchmark.hpp>
|
||
#include <catch2/catch_all.hpp>
|
||
#include <catch2/catch_approx.hpp>
|
||
#include <catch2/catch_test_macros.hpp>
|
||
#include <catch2/matchers/catch_matchers_range_equals.hpp>
|
||
#include <cmath>
|
||
#include <numbers>
|
||
#include <random>
|
||
#include <vector>
|
||
|
||
using namespace Catch;
|
||
|
||
constexpr double TOLERANCE = 1e-4;
|
||
|
||
TEST_CASE("lehmer64 rng")
|
||
{
|
||
s2ga::lehmer64 rng(0);
|
||
|
||
REQUIRE(rng() != 0);
|
||
|
||
const int N = 100;
|
||
|
||
{
|
||
std::vector<int> ivalues;
|
||
rng.seed(4);
|
||
|
||
for(int i = 0; i < N; ++i)
|
||
{
|
||
ivalues.emplace_back(rng.random(0, 256));
|
||
}
|
||
|
||
rng.seed(4);
|
||
|
||
for(int i = 0; i < N; ++i)
|
||
{
|
||
REQUIRE(ivalues[i] == rng.random(0, 256));
|
||
}
|
||
}
|
||
|
||
{
|
||
std::vector<float> fvalues;
|
||
rng.seed(5);
|
||
|
||
for(int i = 0; i < N; ++i)
|
||
{
|
||
fvalues.emplace_back(rng.random(-256.0f, 256.0f));
|
||
}
|
||
|
||
rng.seed(5);
|
||
|
||
for(int i = 0; i < N; ++i)
|
||
{
|
||
REQUIRE(fvalues[i] == rng.random(-256.0f, 256.0f));
|
||
}
|
||
}
|
||
}
|
||
|
||
TEST_CASE("Uniform Distribution Tests")
|
||
{
|
||
s2ga::lehmer64 rng(42); // Fixed seed for reproducibility
|
||
|
||
SECTION("Integer Uniformity - Chi-Squared Test")
|
||
{
|
||
const int min = 0;
|
||
const int max = 9;
|
||
const int num_samples = 1'000'000;
|
||
const int num_bins = max - min + 1;
|
||
const double expected = num_samples / static_cast<double>(num_bins);
|
||
const double critical_value = 16.92; // χ²(0.05, 9)
|
||
|
||
std::vector<int> counts(num_bins, 0);
|
||
for(int i = 0; i < num_samples; ++i)
|
||
{
|
||
int val = rng.random(min, max);
|
||
++counts[val - min];
|
||
}
|
||
|
||
double chi_sq = 0.0;
|
||
for(int count: counts)
|
||
{
|
||
double diff = count - expected;
|
||
chi_sq += (diff * diff) / expected;
|
||
}
|
||
|
||
CHECK(chi_sq < critical_value);
|
||
}
|
||
|
||
SECTION("Floating Point Uniformity - Kolmogorov-Smirnov Test")
|
||
{
|
||
const double min = 0.0;
|
||
const double max = 1.0;
|
||
const int num_samples = 100'000;
|
||
const double ks_critical = 1.36 / std::sqrt(num_samples); // α=0.05
|
||
|
||
std::vector<double> samples(num_samples);
|
||
std::generate(samples.begin(), samples.end(),
|
||
[&] { return rng.random(min, max); });
|
||
|
||
std::sort(samples.begin(), samples.end());
|
||
|
||
double d_plus = 0.0;
|
||
double d_minus = 0.0;
|
||
for(size_t i = 0; i < samples.size(); ++i)
|
||
{
|
||
double fn = (i + 1.0) / num_samples;
|
||
double f = samples[i];
|
||
d_plus = std::max(d_plus, fn - f);
|
||
d_minus = std::max(d_minus, f - (i / (num_samples - 1.0)));
|
||
}
|
||
|
||
double d_stat = std::max(d_plus, d_minus);
|
||
CHECK(d_stat < ks_critical);
|
||
}
|
||
|
||
SECTION("Edge Case Coverage")
|
||
{
|
||
const int iterations = 10'000;
|
||
|
||
// Test minimum and maximum inclusion
|
||
bool hit_min = false;
|
||
bool hit_max = false;
|
||
for(int i = 0; i < iterations; ++i)
|
||
{
|
||
int val = rng.random(1, 10);
|
||
if(val == 1)
|
||
hit_min = true;
|
||
if(val == 10)
|
||
hit_max = true;
|
||
}
|
||
CHECK(hit_min);
|
||
CHECK(hit_max);
|
||
|
||
// Floating point bounds check
|
||
for(int i = 0; i < iterations; ++i)
|
||
{
|
||
double val = rng.random(0.0, 1.0);
|
||
CHECK(val >= 0.0);
|
||
CHECK(val < 1.0);
|
||
}
|
||
}
|
||
}
|
||
|
||
TEST_CASE("random benchmarking", "[benchmark]")
|
||
{
|
||
s2ga::lehmer64 rng(0);
|
||
|
||
const int N = 100'000'000;
|
||
|
||
std::mt19937 std_rng(4);
|
||
std::uniform_int_distribution dist(-512, 512);
|
||
|
||
BENCHMARK("mt19937 100'000'000")
|
||
{
|
||
for(int i = 0; i < N; ++i)
|
||
{
|
||
(void)dist(std_rng);
|
||
}
|
||
};
|
||
|
||
BENCHMARK("lehmer64 100'000'000")
|
||
{
|
||
for(int i = 0; i < N; ++i)
|
||
{
|
||
(void)dist(rng);
|
||
}
|
||
};
|
||
}
|
||
|
||
inline double sphere(double x, double y)
|
||
{
|
||
return std::pow(x, 2.0) + std::pow(y, 2.0);
|
||
}
|
||
|
||
TEST_CASE("sphere(0, 0) = 0")
|
||
{
|
||
REQUIRE(sphere(0.0, 0.0) == Approx(0.0).margin(TOLERANCE));
|
||
}
|
||
|
||
inline double ackley(double x, double y)
|
||
{
|
||
return -20.0 * std::exp(-0.2 * std::sqrt(0.5 * sphere(x, y))) -
|
||
std::exp(0.5 * (std::cos(2.0 * std::numbers::pi * x) +
|
||
std::cos(2.0 * std::numbers::pi * y))) +
|
||
std::numbers::e + 20.0;
|
||
}
|
||
|
||
TEST_CASE("ackley(0, 0) = 0")
|
||
{
|
||
REQUIRE(ackley(0.0, 0.0) == Approx(0.0).margin(TOLERANCE));
|
||
}
|
||
|
||
inline double rastrigin(double x, double y)
|
||
{
|
||
const double A = 10.0;
|
||
return 2.0 * A +
|
||
(std::pow(x, 2.0) - A * std::cos(2.0 * std::numbers::pi * x)) +
|
||
(std::pow(y, 2.0) - A * std::cos(2.0 * std::numbers::pi * y));
|
||
}
|
||
|
||
TEST_CASE("rastrigin(0, 0) = 0")
|
||
{
|
||
REQUIRE(rastrigin(0.0, 0.0) == Approx(0.0).margin(TOLERANCE));
|
||
}
|
||
|
||
inline double rosenbrock(double x, double y)
|
||
{
|
||
return 100.0 * std::pow(y - std::pow(x, 2.0), 2.0) + std::pow(1.0 - x, 2.0);
|
||
}
|
||
|
||
TEST_CASE("rosenbrock(1, 1) = 0")
|
||
{
|
||
REQUIRE(rosenbrock(1.0, 1.0) == Approx(0.0).margin(TOLERANCE));
|
||
}
|
||
|
||
inline double bill(double x, double y)
|
||
{
|
||
return std::pow(1.5 - x + x * y, 2.0) +
|
||
std::pow(2.25 - x + x * std::pow(y, 2.0), 2.0) +
|
||
std::pow(2.625 - x + x * std::pow(y, 3.0), 2.0);
|
||
}
|
||
|
||
TEST_CASE("bill(3, 0.5) = 0")
|
||
{
|
||
REQUIRE(bill(3.0, 0.5) == Approx(0.0).margin(TOLERANCE));
|
||
}
|
||
|
||
inline double goldstein_price(double x, double y)
|
||
{
|
||
return (1.0 + std::pow(x + y + 1.0, 2.0) *
|
||
(19.0 - 14.0 * x + 3.0 * std::pow(x, 2.0) - 14.0 * y +
|
||
6.0 * x * y + 3.0 * std::pow(y, 2.0))) *
|
||
(30.0 + std::pow(2.0 * x - 3.0 * y, 2.0) *
|
||
(18.0 - 32.0 * x + 12.0 * std::pow(x, 2.0) + 48.0 * y -
|
||
36.0 * x * y + 27.0 * std::pow(y, 2.0)));
|
||
}
|
||
|
||
TEST_CASE("goldstein_price(0, -1) = 3")
|
||
{
|
||
REQUIRE(goldstein_price(0.0, -1.0) == Approx(3.0).margin(TOLERANCE));
|
||
}
|
||
|
||
inline double booth(double x, double y)
|
||
{
|
||
return std::pow(x + 2.0 * y - 7.0, 2.0) + std::pow(2.0 * x + y - 5.0, 2.0);
|
||
}
|
||
|
||
TEST_CASE("booth(1, 3) = 0")
|
||
{
|
||
REQUIRE(booth(1.0, 3.0) == Approx(0.0).margin(TOLERANCE));
|
||
}
|
||
|
||
inline double bukin_n6(double x, double y)
|
||
{
|
||
return 100.0 * std::sqrt(std::abs(y - 0.01 * std::pow(x, 2.0))) +
|
||
0.01 * std::abs(x + 10.0);
|
||
}
|
||
|
||
TEST_CASE("bukin_n6(-10, 1) = 0")
|
||
{
|
||
REQUIRE(bukin_n6(-10.0, 1.0) == Approx(0.0).margin(TOLERANCE));
|
||
}
|
||
|
||
inline double matyas(double x, double y)
|
||
{
|
||
return 0.26 * sphere(x, y) - 0.48 * x * y;
|
||
}
|
||
|
||
TEST_CASE("matyas(0, 0) = 0")
|
||
{
|
||
REQUIRE(matyas(0.0, 0.0) == Approx(0.0).margin(TOLERANCE));
|
||
}
|
||
|
||
inline double sin2(double x)
|
||
{
|
||
return std::pow(std::sin(x), 2.0);
|
||
}
|
||
|
||
inline double levi_n13(double x, double y)
|
||
{
|
||
return sin2(3.0 * std::numbers::pi * x) +
|
||
std::pow(x - 1.0, 2.0) * (1.0 + sin2(3.0 * std::numbers::pi * y)) +
|
||
std::pow(y - 1.0, 2.0) * (1.0 + sin2(2.0 * std::numbers::pi * y));
|
||
}
|
||
|
||
TEST_CASE("levi_n13(1, 1) = 0")
|
||
{
|
||
REQUIRE(levi_n13(1.0, 1.0) == Approx(0.0).margin(TOLERANCE));
|
||
}
|
||
|
||
inline double three_hump_camel(double x, double y)
|
||
{
|
||
return 2.0 * std::pow(x, 2.0) - 1.05 * std::pow(x, 4.0) +
|
||
std::pow(x, 6.0) / 6.0 + x * y + std::pow(y, 2.0);
|
||
}
|
||
|
||
TEST_CASE("three_hump_camel(0, 0) = 0")
|
||
{
|
||
REQUIRE(three_hump_camel(0.0, 0.0) == Approx(0.0).margin(TOLERANCE));
|
||
}
|
||
|
||
inline double eggholder(double x, double y)
|
||
{
|
||
return -(y + 47.0) * std::sin(std::sqrt(std::abs(x / 2.0 + (y + 47.0)))) -
|
||
x * std::sin(std::sqrt(std::abs(x - (y + 47.0))));
|
||
}
|
||
|
||
TEST_CASE("eggholder(512, 404.2319) = -959.6407")
|
||
{
|
||
REQUIRE(eggholder(512.0, 404.2319) == Approx(-959.6407).margin(TOLERANCE));
|
||
}
|
||
|
||
inline double mccormick(double x, double y)
|
||
{
|
||
return std::sin(x + y) + std::pow(x - y, 2.0) - 1.5 * x + 2.5 * y + 1.0;
|
||
}
|
||
|
||
TEST_CASE("mccormick(-0.54719, -1.54719) = -1.9133")
|
||
{
|
||
REQUIRE(mccormick(-0.54719, -1.54719) == Approx(-1.9133).margin(TOLERANCE));
|
||
}
|
||
|
||
inline double schaffer_n2(double x, double y)
|
||
{
|
||
return 0.5 + (sin2(std::pow(x, 2.0) - std::pow(y, 2.0)) - 0.5) /
|
||
std::pow(1.0 + 0.001 * sphere(x, y), 2.0);
|
||
}
|
||
|
||
TEST_CASE("schaffer_n2(0, 0) = 0")
|
||
{
|
||
REQUIRE(schaffer_n2(0.0, 0.0) == Approx(0.0).margin(TOLERANCE));
|
||
}
|
||
|
||
inline double cos2(double x)
|
||
{
|
||
return std::pow(std::cos(x), 2.0);
|
||
}
|
||
|
||
inline double schaffer_n4(double x, double y)
|
||
{
|
||
return 0.5 +
|
||
(cos2(std::sin(std::abs(std::pow(x, 2.0) - std::pow(y, 2.0)))) -
|
||
0.5) /
|
||
std::pow(1.0 + 0.001 * sphere(x, y), 2.0);
|
||
}
|
||
|
||
TEST_CASE("schaffer_n4(0, 1.25313) = 0.292579")
|
||
{
|
||
REQUIRE(schaffer_n4(0.0, 1.25313) == Approx(0.292579).margin(TOLERANCE));
|
||
}
|
||
|
||
TEST_CASE("Should pass")
|
||
{
|
||
REQUIRE_NOTHROW(foo());
|
||
}
|