s2ga/tests/test.cpp

#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", "[test]")
{
    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", "[test]")
{
    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", "[test]")
{
    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", "[test]")
{
    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", "[test]")
{
    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", "[test]")
{
    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", "[test]")
{
    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", "[test]")
{
    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", "[test]")
{
    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", "[test]")
{
    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", "[test]")
{
    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", "[test]")
{
    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", "[test]")
{
    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", "[test]")
{
    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", "[test]")
{
    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", "[test]")
{
    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", "[test]")
{
    REQUIRE(schaffer_n4(0.0, 1.25313) == Approx(0.292579).margin(TOLERANCE));
}

TEST_CASE("Should pass", "[test]")
{
    REQUIRE_NOTHROW(foo());
}