#include <array>
#include <cmath>
#include <concepts>
#include <limits>
#include <type_traits>

#include <catch2/catch_test_macros.hpp>
#include <catch2/matchers/catch_matchers_floating_point.hpp>

import mean_field;
import test_helpers;

namespace {
    namespace eos = mean_field::eos;

    template <typename Candidate>
    concept HasAnyUnaryEquationOfStateConversion =
        requires(const Candidate &candidate, const double value) { candidate.pressure_from_density(value); } ||
        requires(const Candidate &candidate, const double value) { candidate.pressure_from_enthalpy(value); } ||
        requires(const Candidate &candidate, const double value) { candidate.enthalpy_from_density(value); } ||
        requires(const Candidate &candidate, const double value) { candidate.enthalpy_from_pressure(value); } ||
        requires(const Candidate &candidate, const double value) { candidate.density_from_enthalpy(value); } ||
        requires(const Candidate &candidate, const double value) {
            candidate.density_derivative_from_enthalpy(value);
        } ||
        requires(const Candidate &candidate, const double value) {
            candidate.pressure_derivative_from_enthalpy(value);
        } ||
        requires(const Candidate &candidate, const double value) { candidate.pressure_derivative_from_density(value); };
} // namespace

TEST_CASE(
    "Polytropic EOS Declares Its Thermodynamic Relation Contract",
    tags::polytropic_eos_relation_contract
) {
    using Polytrope = eos::Polytrope;

    STATIC_CHECK(eos::EquationOfStateModel<Polytrope>);
    STATIC_CHECK_FALSE(std::is_polymorphic_v<Polytrope>);
    STATIC_CHECK_FALSE(HasAnyUnaryEquationOfStateConversion<Polytrope>);
    STATIC_CHECK(Polytrope::Relations::size == 5);

    STATIC_CHECK(eos::SupportsRelation<Polytrope, eos::PressureFromDensity>);
    STATIC_CHECK(eos::SupportsRelation<Polytrope, eos::PressureFromSpecificEnthalpy>);
    STATIC_CHECK(eos::SupportsRelation<Polytrope, eos::SpecificEnthalpyFromDensity>);
    STATIC_CHECK(eos::SupportsRelation<Polytrope, eos::SpecificEnthalpyFromPressure>);
    STATIC_CHECK(eos::SupportsRelation<Polytrope, eos::DensityFromSpecificEnthalpy>);

    STATIC_CHECK(eos::SupportsPartialDerivative<Polytrope, eos::PressureFromDensity, eos::quantity::Density>);
    STATIC_CHECK(
        eos::SupportsPartialDerivative<Polytrope, eos::PressureFromSpecificEnthalpy, eos::quantity::SpecificEnthalpy>
    );
    STATIC_CHECK(
        eos::SupportsPartialDerivative<Polytrope, eos::DensityFromSpecificEnthalpy, eos::quantity::SpecificEnthalpy>
    );

    STATIC_CHECK_FALSE(
        eos::SupportsPartialDerivative<Polytrope, eos::SpecificEnthalpyFromPressure, eos::quantity::Pressure>
    );
    STATIC_CHECK_FALSE(
        eos::SupportsPartialDerivative<Polytrope, eos::SpecificEnthalpyFromDensity, eos::quantity::Density>
    );
}

TEST_CASE(
    "Polytropic EOS Typed Relations Preserve Analytic Values",
    tags::polytropic_eos_characterization
) {
    constexpr std::array<double, 3> polytropicIndices{1.0, 1.5, 3.0};
    constexpr std::array<double, 2> polytropicConstants{0.25, 0.73};
    constexpr std::array<double, 4> densities{0.0, 1.0e-6, 0.2, 2.0};
    constexpr std::array<double, 4> specificEnthalpies{-0.3, 0.0, 0.2, 1.7};
    constexpr std::array<double, 4> pressures{0.0, 1.0e-8, 0.3, 4.0};

    for (const double polytropicIndex : polytropicIndices) {
        for (const double polytropicConstant : polytropicConstants) {
            const eos::Polytrope equationOfState(polytropicIndex, polytropicConstant);

            for (const double density : densities) {
                CAPTURE(polytropicIndex, polytropicConstant, density);

                const double expectedPressure = polytropicConstant * std::pow(density, 1.0 + 1.0 / polytropicIndex);
                const double expectedSpecificEnthalpy =
                    (polytropicIndex + 1.0) * polytropicConstant * std::pow(density, 1.0 / polytropicIndex);

                CHECK(
                    eos::evaluate<eos::quantity::Pressure>(equationOfState, eos::DensityValue{density}).value() ==
                    expectedPressure
                );

                CHECK(
                    eos::evaluate<eos::quantity::SpecificEnthalpy>(equationOfState, eos::DensityValue{density})
                        .value() == expectedSpecificEnthalpy
                );

                CHECK_THAT(
                    (eos::partialDerivative<eos::quantity::Pressure, eos::quantity::Density>(
                         equationOfState, eos::DensityValue{density}
                    )
                         .value()),
                    Catch::Matchers::WithinRel(
                        density == 0.0 ? 0.0 : expectedSpecificEnthalpy / polytropicIndex, 2.0e-15
                    )
                );
            }

            for (const double specificEnthalpy : specificEnthalpies) {
                CAPTURE(polytropicIndex, polytropicConstant, specificEnthalpy);

                const double expectedDensity =
                    specificEnthalpy <= 0.0
                        ? 0.0
                        : std::pow(specificEnthalpy / ((polytropicIndex + 1.0) * polytropicConstant), polytropicIndex);

                CHECK(
                    eos::evaluate<eos::quantity::Density>(equationOfState, eos::SpecificEnthalpyValue{specificEnthalpy})
                        .value() == expectedDensity
                );

                CHECK(
                    eos::evaluate<eos::quantity::Pressure>(
                        equationOfState, eos::SpecificEnthalpyValue{specificEnthalpy}
                    )
                        .value() ==
                    (specificEnthalpy <= 0.0 ? 0.0 : expectedDensity * specificEnthalpy / (polytropicIndex + 1.0))
                );

                CHECK(
                    (eos::partialDerivative<eos::quantity::Pressure, eos::quantity::SpecificEnthalpy>(
                         equationOfState, eos::SpecificEnthalpyValue{specificEnthalpy}
                     )
                         .value() == expectedDensity)
                );
            }

            for (const double pressure : pressures) {
                CAPTURE(polytropicIndex, polytropicConstant, pressure);

                const double indexPlusOne             = polytropicIndex + 1.0;
                const double expectedSpecificEnthalpy = indexPlusOne *
                                                        std::pow(polytropicConstant, polytropicIndex / indexPlusOne) *
                                                        std::pow(pressure, 1.0 / indexPlusOne);

                CHECK(
                    eos::evaluate<eos::quantity::SpecificEnthalpy>(equationOfState, eos::PressureValue{pressure})
                        .value() == expectedSpecificEnthalpy
                );
            }
        }
    }
}

TEST_CASE(
    "Typed Polytropic EOS Preserves Domain And Exterior Semantics",
    tags::polytropic_eos_relation_contract
) {
    const eos::Polytrope equationOfState(3.0, 0.75);

    try {
        static_cast<void>(eos::evaluate<eos::quantity::Pressure>(equationOfState, eos::DensityValue{-0.1}));
        FAIL("A negative density must be rejected.");
    } catch (const eos::EvaluationError &error) {
        CHECK(error.code() == eos::EvaluationErrorCode::outside_domain);
    }

    try {
        static_cast<void>(eos::evaluate<eos::quantity::SpecificEnthalpy>(
            equationOfState, eos::PressureValue{std::numeric_limits<double>::quiet_NaN()}
        ));
        FAIL("A nonfinite pressure must be rejected.");
    } catch (const eos::EvaluationError &error) {
        CHECK(error.code() == eos::EvaluationErrorCode::nonfinite_input);
    }

    constexpr double exteriorSpecificEnthalpy = -0.3;

    CHECK(
        eos::evaluate<eos::quantity::Density>(equationOfState, eos::SpecificEnthalpyValue{exteriorSpecificEnthalpy})
            .value() == 0.0
    );

    CHECK(
        eos::evaluate<eos::quantity::Pressure>(equationOfState, eos::SpecificEnthalpyValue{exteriorSpecificEnthalpy})
            .value() == 0.0
    );

    CHECK(
        (eos::partialDerivative<eos::quantity::Density, eos::quantity::SpecificEnthalpy>(
             equationOfState, eos::SpecificEnthalpyValue{exteriorSpecificEnthalpy}
         )
             .value() == 0.0)
    );

    CHECK(
        (eos::partialDerivative<eos::quantity::Pressure, eos::quantity::SpecificEnthalpy>(
             equationOfState, eos::SpecificEnthalpyValue{exteriorSpecificEnthalpy}
         )
             .value() == 0.0)
    );
}