#include <cmath>
#include <limits>

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

#include "serif/eos/evaluation.hpp"
#include "serif/eos/exceptions.hpp"
#include "serif/eos/models/polytropic.hpp"

namespace eos = serif::eos;
namespace dimensions = serif::dimensions;

TEST_CASE("Polytropic pressure potential obeys its mechanical derivative contract", "[eos][barotropic_density][unit]") {
    for (const double index : {1.0, 1.5, 2.0, 2.5, 3.0}) {
        const eos::models::Polytrope model{index, 0.73};
        for (const double density : {1.0e-6, 0.2, 2.0}) {
            CAPTURE(index, density);
            const dimensions::DensityValue state{density};
            const double potential = eos::evaluate<dimensions::BarotropicPressurePotential>(model, state).value();
            CHECK_THAT(potential, Catch::Matchers::WithinRel((index + 1.0) * 0.73 * std::pow(density, 1.0 / index), 2.0e-15));
            const double step = density * 1.0e-4;
            const double positive = eos::evaluate<dimensions::BarotropicPressurePotential>(model, dimensions::DensityValue{density + step}).value();
            const double negative = eos::evaluate<dimensions::BarotropicPressurePotential>(model, dimensions::DensityValue{density - step}).value();
            const double expected_slope = eos::partial_derivative<dimensions::Pressure, dimensions::MassDensity>(model, state).value() / density;
            CHECK_THAT((positive - negative) / (2.0 * step), Catch::Matchers::WithinRel(expected_slope, 3.0e-9));
        }
        CHECK(eos::evaluate<dimensions::BarotropicPressurePotential>(model, dimensions::DensityValue{0.0}).value() == 0.0);
        for (const double invalid : {-0.1, std::numeric_limits<double>::infinity(), std::numeric_limits<double>::quiet_NaN()}) {
            CHECK_THROWS_AS(eos::evaluate<dimensions::BarotropicPressurePotential>(model, dimensions::DensityValue{invalid}), eos::EOSEvaluationError);
        }
    }
}