MeanField_SERiF/src/include/serif/dimensions/partial.hpp

#pragma once

/**
 * @file partial.hpp
 * @author Emily M. Boudreaux
 *
 * @brief Compile time tools to represent a partial derivative of one quantity wrt. another quantity.
 * Note that this system is not responsible for computing partials or in fact derivatives of any kind.
 * Rather, it is responsible for forcing the developer --- or compiler at least --- to ask
 * for a specific, explicit, partial and have to spell out what that is. That in turn gives
 * the compiler enough information to do a lot of downstream things. A motivating example would be automatic verification
 * of the provided EOS against all partials that might be needed to ensure they are all exported
 * by the EOS.
 */

#include "serif/dimensions/quantities.hpp"
#include "serif/utils/misc/concepts/numeric.hpp"

namespace serif::dimensions {
    /**
     * @struct WithRespectTo
     *
     * @tparam Quantity A quantity satisfying @ref ThermodynamicQuantityType
     * @brief A type that is empty at runtime but allows for the developer
     * to specify to the compiler what quantity the partial is with respect to.
     */
    template <ThermodynamicQuantityType Quantity>
    struct WithRespectTo final {};

    /**
     * @class PartialDerivative
     *
     * @tparam OutputQuantity
     * @tparam InputQuantity
     *
     * @brief Class to represent a compile time derivative relation between two quantities. Note that
     * this class does not, in fact cannot, compute any derivatives itself. Rather, this is a way
     * for the compiler to understand higher level mathematical relations. Unless you are really
     * in the weeds of the development team you will likely not need to interact with this
     * directly. Further note that this class does include (unlike the more basic dimension system)
     * some basic dimensional analysis. Specifically, there are some overloaded operators that
     * allow for certain specializations of PartialDerivative to operate on one and other
     * conditioned on what their input and output types are. This does not do any thing like
     * convert area to length^2. However, it will do more basic things like ensure that you
     * can only add two partials which agree on their dimensions exactly. Or that while you can
     * multiple a partial by any scalar, you cannot multiply arbitrary partials.
     */
    template <ThermodynamicQuantityType OutputQuantity, ThermodynamicQuantityType InputQuantity>
    class PartialDerivative final {
    public:
        explicit constexpr PartialDerivative(const double value) noexcept : m_value(value){}

        /**
         * @brief Get the underlying value as a compile time constant if possible. This
         * allows the compiler, where the constructor may be determined at compile time,
         * to fully optimize PartialDerivative operations as if they were doubles.
         *
         * @note calling value gets the underlying numeric value directly thereby bypassing
         * the limitations on what a valid operation are (e.g. what the operator overloads
         * enforce).
         *
         * @return m_value: This is whatever was passed at constructor time since there is
         * no way to modify this value after construction without some truly horrific C++ tricks
         */
        [[nodiscard]] constexpr double value() const noexcept {
            return m_value;
        }

        /**
         * @brief Overload the + operator between two partials which share the exact same input
         * and output types
         * @param lhs One partial
         * @param rhs Other Partial
         * @return A new partial with the same input and output types where m_value = lhs.m_value + rhs.m_value
         */
        friend constexpr PartialDerivative<OutputQuantity, InputQuantity> operator+(
            const PartialDerivative<OutputQuantity, InputQuantity>& lhs,
            const PartialDerivative<OutputQuantity, InputQuantity>& rhs
        ) noexcept {
            return PartialDerivative<OutputQuantity, InputQuantity>{lhs.m_value + rhs.m_value};
        }

        /**
         * @brief Overload the - operator between two partials which share the exact same input
         * and output types
         * @param lhs One partial
         * @param rhs Other Partial
         * @return A new partial with the same input and output types where m_value = lhs.m_value - rhs.m_value
         */
        friend constexpr PartialDerivative<OutputQuantity, InputQuantity> operator-(
            const PartialDerivative<OutputQuantity, InputQuantity>& lhs,
            const PartialDerivative<OutputQuantity, InputQuantity>& rhs
        ) noexcept {
            return PartialDerivative<OutputQuantity, InputQuantity>{lhs.m_value - rhs.m_value};
        }

        /**
         * @brief Overload of the * operator for a left partial and a right scalar
         * and output types
         * @tparam Scalar Any value satisfying the @ref IsNumeric concept (integral types and float types)
         * @param lhs Partial with some input and some output type
         * @param rhs Some numeric quantity
         * @return A new partial with the same input and output types where m_value = lhs.m_value * rhs
         */
        template <utils::misc::concepts::IsNumeric Scalar>
        friend constexpr PartialDerivative<OutputQuantity, InputQuantity> operator*(
            const PartialDerivative<OutputQuantity, InputQuantity>& lhs,
            const Scalar& rhs
        ) noexcept {
            return PartialDerivative<OutputQuantity, InputQuantity>{lhs.m_value * rhs};
        }

        /**
         * @brief Overload of the * operator for a right partial and a left scalar
         * and output types
         * @tparam Scalar Any value satisfying the @ref IsNumeric concept (integral types and float types)
         * @param lhs Some numeric quantity
         * @param rhs Partial with some input and some output type
         * @return A new partial with the same input and output types where m_value = lhs * rhs.m_value
         */
        template <utils::misc::concepts::IsNumeric Scalar>
        friend constexpr PartialDerivative<OutputQuantity, InputQuantity> operator*(
            const Scalar& lhs,
            const PartialDerivative<OutputQuantity, InputQuantity>& rhs
        ) noexcept {
            return PartialDerivative<OutputQuantity, InputQuantity>{lhs * rhs.m_value};
        }

        /**
         * @brief Overload of the / operator for a left partial and a right scalar
         * and output types
         * @tparam Scalar Any value satisfying the @ref IsNumeric concept (integral types and float types)
         * @param lhs Partial with some input and some output type
         * @param rhs Some numeric quantity
         * @return A new partial with the same input and output types where m_value = lhs.m_value / rhs
         */
        template <utils::misc::concepts::IsNumeric Scalar>
        friend constexpr PartialDerivative<OutputQuantity, InputQuantity> operator/(
            const PartialDerivative<OutputQuantity, InputQuantity>& lhs,
            const Scalar& rhs
        ) noexcept {
            return PartialDerivative<OutputQuantity, InputQuantity>{lhs.m_value / rhs};
        }

        /**
         * @brief Partial ordering overload to compare a left partial and a right scalar
         * @tparam Scalar Any value satisfying the @ref IsNumeric concept (integral types and float types)
         * @param lhs Some numeric quantity
         * @param rhs Some partial with an input and output type
         * @return partial ordering comparing rhs.m_value to lhs
         */
        template <utils::misc::concepts::IsNumeric Scalar>
        friend constexpr std::partial_ordering operator<=>(
            const PartialDerivative<OutputQuantity, InputQuantity>& lhs,
            Scalar rhs
        ) noexcept {
            return lhs.m_value <=> rhs;
        }

        /**
         * @brief Partial ordering overload to compare a right partial and a left scalar
         * @tparam Scalar Any value satisfying the @ref IsNumeric concept (integral types and float types)
         * @param lhs Some numeric quantity
         * @param rhs Some partial with an input and output type
         * @return partial ordering comparing rhs.m_value to lhs
         */
        template <utils::misc::concepts::IsNumeric Scalar>
        friend constexpr std::partial_ordering operator<=>(
            Scalar lhs,
            const PartialDerivative<OutputQuantity, InputQuantity>& rhs
        ) noexcept {
            return lhs <=> rhs.m_value;
        }

        /**
         * @brief Partial ordering comparing two partials with exactly the same input and output types
         * @param lhs Some Partial
         * @param rhs Other Partial
         * @return Partial ordering comparing lhs.m_value to rhs.m_value
         */
        friend constexpr std::partial_ordering operator<=>(
            const PartialDerivative<OutputQuantity, InputQuantity> &lhs,
            const PartialDerivative<OutputQuantity, InputQuantity> &rhs
        ) noexcept {
            return lhs.m_value <=> rhs.m_value;
        }

    private:
        double m_value; ///< Numeric value associated with the partial. If this is known at compile time then the compiler can optimize operations with partial.value() to be equivalent to compile time double operations.
    };
}