/*
 * @brief Defines and implements classes to define physical SI units
 * @file types/Quantity.hpp
 * @author Sven Czarnian <devel@svcz.de>
 * @copyright Copyright 2020-2021 Sven Czarnian
 * @license This project is published under the GNU General Public License v3 (GPLv3)
 */

#pragma once

#include <cmath>
#include <ratio>

#include <aman/helper/Math.h>

namespace aman {
    /**
     * @brief Defines the base class to define different physical SI units
     * @ingroup types
     *
     * The template arguments are used to define the exponent of the SI unit.
     * These Quantity definitions are the base to describe all physical relations.
     *
     * By use of this implementation is it possible to ensure, that the SI units
     * are as expected after the calculations.
     *
     * This avoids logical errors and it is useful to avoid the auto-keyword otherwise
     * is it not possible to check the correctness of the SI units.
     *
     * @tparam M The exponent of the mass parts
     * @tparam L The exponent of the length parts
     * @tparam T The exponent of the time parts
     * @tparam A The exponent of the angular parts
     */
    template <typename M, typename L, typename T, typename A>
    class Quantity {
    private:
        float m_value;

    public:
        /**
         * @brief Initializes a quantity with the default value
         */
        constexpr Quantity() noexcept : m_value(0.0f) { }
        /**
         * @brief Initializes the quantity with a given value
         * @param[in] value The set value
         */
        explicit constexpr Quantity(float value) : m_value(value) { }

        /**
         * @brief Adds rhs into this instance and returns the updated instance
         * @param[in] rhs The right-hand-side component
         * @return The resulting quantity with the updated value
         */
        constexpr Quantity const& operator+=(const Quantity& rhs) {
            this->m_value += rhs.m_value;
            return *this;
        }
        /**
         * @brief Substracts rhs into this instance and returns the updated instance
         * @param[in] rhs The right-hand-side component
         * @return The resulting quantity with the updated value
         */
        constexpr Quantity const& operator-=(const Quantity& rhs) {
            this->m_value -= rhs.m_value;
            return *this;
        }

        /**
         * @brief Returns the value in SI units
         * @return The contained value
         */
        constexpr float value() const {
            return this->m_value;
        }
        /**
         * @brief Sets the value in SI units
         * @param[in] value The new SI unit based value
         */
        constexpr void setValue(float value) {
            this->m_value = value;
        }
        /**
         * @brief Converts the value into a specific unit
         * @param[in] rhs The scaling factor to convert the value
         * @return The converted value
         */
        constexpr float convert(const Quantity& rhs) const {
            return this->m_value / rhs.m_value;
        }
        /**
         * @brief Calculates the square-root and updates the SI units as well
         * @return The resulting instance with updated template arguments
         */
        constexpr Quantity<std::ratio_divide<M, std::ratio<2>>, std::ratio_divide<L, std::ratio<2>>,
                           std::ratio_divide<T, std::ratio<2>>, std::ratio_divide<A, std::ratio<2>>> sqrt() const {
            return Quantity<std::ratio_divide<M, std::ratio<2>>, std::ratio_divide<L, std::ratio<2>>,
                            std::ratio_divide<T, std::ratio<2>>, std::ratio_divide<A, std::ratio<2>>>(std::sqrtf(this->m_value));
        }
        /**
         * @brief Calculates the absolute of the contained value and returns it as a new Quantity instance
         * @return The absolute value instance
         */
        constexpr Quantity<M, L, T, A> abs() const {
            return Quantity<M, L, T, A>(std::abs(this->m_value));
        }
    };

    /** The mass specialization [kg] */
    typedef Quantity<std::ratio<1>, std::ratio<0>, std::ratio<0>, std::ratio<0>>  Mass;
    /** The length specialization [m] */
    typedef Quantity<std::ratio<0>, std::ratio<1>, std::ratio<0>, std::ratio<0>>  Length;
    /** The time specialization [s] */
    typedef Quantity<std::ratio<0>, std::ratio<0>, std::ratio<1>, std::ratio<0>>  Time;
    /** The angle specialization [rad] */
    typedef Quantity<std::ratio<0>, std::ratio<0>, std::ratio<0>, std::ratio<1>>  Angle;
    /** The velocity specialization [m/s] */
    typedef Quantity<std::ratio<0>, std::ratio<1>, std::ratio<-1>, std::ratio<0>> Velocity;
    /** The acceleration specialization [m/(s*s)] */
    typedef Quantity<std::ratio<0>, std::ratio<1>, std::ratio<-2>, std::ratio<0>> Acceleration;
    /** The angular velocity specialization [1/s] */
    typedef Quantity<std::ratio<0>, std::ratio<0>, std::ratio<-1>, std::ratio<1>> AngularVelocity;
    /** The angular acceleration specialization [1/(s*s)] */
    typedef Quantity<std::ratio<0>, std::ratio<0>, std::ratio<-2>, std::ratio<1>> AngularAcceleration;

    /**
     * @brief Adds rhs to lhs and returns a new instance
     * @param[in] lhs The left-hand-side component
     * @param[in] rhs The right-hand-side component
     * @return The resulting quantity with the updated value
     */
    template <typename M, typename L, typename T, typename A>
    constexpr Quantity<M, L, T, A> operator+(const Quantity<M, L, T, A>& lhs, const Quantity<M, L, T, A>& rhs) {
        return Quantity<M, L, T, A>(lhs.value() + rhs.value());
    }
    /**
     * @brief Substracts rhs to lhs and returns a new instance
     * @param[in] lhs The left-hand-side component
     * @param[in] rhs The right-hand-side component
     * @return The resulting quantity with the updated value
     */
    template <typename M, typename L, typename T, typename A>
    constexpr Quantity<M, L, T, A> operator-(const Quantity<M, L, T, A>& lhs, const Quantity<M, L, T, A>& rhs) {
        return Quantity<M, L, T, A>(lhs.value() - rhs.value());
    }
    /**
     * @brief Multiplies rhs to lhs and returns a new instance
     * @param[in] lhs The left-hand-side component
     * @param[in] rhs The right-hand-side component
     * @return The resulting quantity with the updated value
     */
    template <typename M1, typename L1, typename T1, typename A1,
              typename M2, typename L2, typename T2, typename A2>
    constexpr Quantity<std::ratio_add<M1, M2>, std::ratio_add<L1, L2>,
                       std::ratio_add<T1, T2>, std::ratio_add<A1, A2>>
            operator*(const Quantity<M1, L1, T1, A1>& lhs, const Quantity<M2, L2, T2, A2>& rhs) {
        return Quantity<std::ratio_add<M1, M2>, std::ratio_add<L1, L2>,
                        std::ratio_add<T1, T2>, std::ratio_add<A1, A2>>(lhs.value() * rhs.value());
    }
    /**
     * @brief Multiplies lhs to rhs and returns a new instance
     * @param[in] lhs The SI-unit free factor
     * @param[in] rhs The right-hand-side component
     * @return The resulting quantity with the updated value
     */
    template <typename M, typename L, typename T, typename A>
    constexpr Quantity<M, L, T, A> operator*(const float& lhs, const Quantity<M, L, T, A>& rhs) {
        return Quantity<M, L, T, A>(lhs * rhs.value());
    }
    /**
     * @brief Multiplies rhs to lhs and returns a new instance
     * @param[in] lhs The left-hand-side component
     * @param[in] rhs The SI-unit free factor
     * @return The resulting quantity with the updated value
     */
    template <typename M, typename L, typename T, typename A>
    constexpr Quantity<M, L, T, A> operator*(const Quantity<M, L, T, A>& lhs, const float& rhs) {
        return Quantity<M, L, T, A>(lhs.value() * rhs);
    }
    /**
     * @brief Divides rhs from lhs and returns a new instance
     * @param[in] lhs The left-hand-side component
     * @param[in] rhs The right-hand-side component
     * @return The resulting quantity with the updated value
     */
    template <typename M1, typename L1, typename T1, typename A1,
              typename M2, typename L2, typename T2, typename A2>
    constexpr Quantity<std::ratio_subtract<M1, M2>, std::ratio_subtract<L1, L2>,
                       std::ratio_subtract<T1, T2>, std::ratio_subtract<A1, A2>>
            operator/(const Quantity<M1, L1, T1, A1>& lhs, const Quantity<M2, L2, T2, A2>& rhs) {
        return Quantity<std::ratio_subtract<M1, M2>, std::ratio_subtract<L1, L2>,
                        std::ratio_subtract<T1, T2>, std::ratio_subtract<A1, A2>>(lhs.value() / rhs.value());
    }
    /**
     * @brief Divides rhs from lhs and returns a new instance
     * @param[in] lhs The SI-unit free factor
     * @param[in] rhs The right-hand-side component
     * @return The resulting quantity with the updated value
     */
    template <typename M, typename L, typename T, typename A>
    constexpr Quantity<std::ratio_subtract<std::ratio<0>, M>, std::ratio_subtract<std::ratio<0>, L>,
                       std::ratio_subtract<std::ratio<0>, T>, std::ratio_subtract<std::ratio<0>, A>>
            operator/(const float& lhs, const Quantity<M, L, T, A>& rhs) {
        return Quantity<std::ratio_subtract<std::ratio<0>, M>, std::ratio_subtract<std::ratio<0>, L>,
                        std::ratio_subtract<std::ratio<0>, T>, std::ratio_subtract<std::ratio<0>, A>>(lhs / rhs.value());
    }
    /**
     * @brief Multiplies lhs from rhs and returns a new instance
     * @param[in] lhs The left-hand-side component
     * @param[in] rhs The SI-unit free factor
     * @return The resulting quantity with the updated value
     */
    template <typename M, typename L, typename T, typename A>
    constexpr Quantity<M, L, T, A> operator/(const Quantity<M, L, T, A>& lhs, const float& rhs) {
        return Quantity<M, L, T, A>(lhs.value() / rhs);
    }

    /**
     * @brief Compares if two instance are equal or almost equal
     * @param[in] lhs The left-hand-side component
     * @param[in] rhs The right-hand-side component
     * @return True if the instances are almost equal, else false
     */
    template <typename M, typename L, typename T, typename A>
    constexpr bool operator==(const Quantity<M, L, T, A>& lhs, const Quantity<M, L, T, A>& rhs) {
        return true == Math::almostEqual(lhs.value(), rhs.value(), 1e-8f);
    }
    /**
     * @brief Compares if two instance are not equal
     * @param[in] lhs The left-hand-side component
     * @param[in] rhs The right-hand-side component
     * @return True if the instances are not equal
     */
    template <typename M, typename L, typename T, typename A>
    constexpr bool operator!=(const Quantity<M, L, T, A>& lhs, const Quantity<M, L, T, A>& rhs) {
        return false == Math::almostEqual(lhs.value(), rhs.value(), 1e-8f);
    }
    /**
     * @brief Compares if lhs is smaller or equal compared to rhs
     * @param[in] lhs The left-hand-side component
     * @param[in] rhs The right-hand-side component
     * @return True if lhs is smaller or equal compared to rhs
     */
    template <typename M, typename L, typename T, typename A>
    constexpr bool operator<=(const Quantity<M, L, T, A>& lhs, const Quantity<M, L, T, A>& rhs) {
        return lhs.value() <= rhs.value();
    }
    /**
     * @brief Compares if lhs is smaller compared to rhs
     * @param[in] lhs The left-hand-side component
     * @param[in] rhs The right-hand-side component
     * @return True if lhs is smaller compared to rhs
     */
    template <typename M, typename L, typename T, typename A>
    constexpr bool operator<(const Quantity<M, L, T, A>& lhs, const Quantity<M, L, T, A>& rhs) {
        return lhs.value() < rhs.value();
    }
    /**
     * @brief Compares if lhs is greater or equal compared to rhs
     * @param[in] lhs The left-hand-side component
     * @param[in] rhs The right-hand-side component
     * @return True if lhs is greater or equal compared to rhs
     */
    template <typename M, typename L, typename T, typename A>
    constexpr bool operator>=(const Quantity<M, L, T, A>& lhs, const Quantity<M, L, T, A>& rhs) {
        return lhs.value() >= rhs.value();
    }
    /**
     * @brief Compares if lhs is greater compared to rhs
     * @param[in] lhs The left-hand-side component
     * @param[in] rhs The right-hand-side component
     * @return True if lhs is greater compared to rhs
     */
    template <typename M, typename L, typename T, typename A>
    constexpr bool operator>(const Quantity<M, L, T, A>& lhs, const Quantity<M, L, T, A>& rhs) {
        return lhs.value() > rhs.value();
    }

    /**< Defines a kilogram */
    constexpr Mass kilogram(1.0f);
    constexpr Mass pound = 0.453592f * kilogram;
    /**< Defines the literal of kilograms */
    constexpr Mass operator"" _kg(long double value) { return Mass(static_cast<float>(value)); }
    /**< Defines the literal of kilograms */
    constexpr Mass operator"" _kg(unsigned long long int value) { return Mass(static_cast<float>(value)); }
    /**< Defines the literal of pounds */
    constexpr Mass operator"" _lbs(long double value) { return static_cast<float>(value) * pound; }
    /**< Defines the literal of pounds */
    constexpr Mass operator"" _lbs(unsigned long long int value) { return static_cast<float>(value) * pound; }

    /**< Defines a metres */
    constexpr Length metre(1.0f);
    /**< Defines a feet */
    constexpr Length feet = 0.3048f * metre;
    /**< Defines a kilometres */
    constexpr Length kilometre = 1000.0f * metre;
    /**< Defines a nautical mile */
    constexpr Length nauticmile = 1852.0f * metre;
    /**< Defines the literal of metres */
    constexpr Length operator"" _m(long double value) { return Length(static_cast<float>(value)); }
    /**< Defines the literal of metres */
    constexpr Length operator"" _m(unsigned long long int value) { return Length(static_cast<float>(value)); }
    /**< Defines the literal of feets */
    constexpr Length operator"" _ft(long double value) { return static_cast<float>(value) * feet; }
    /**< Defines the literal of feets */
    constexpr Length operator"" _ft(unsigned long long int value) { return static_cast<float>(value) * feet; }
    /**< Defines the literal of kilometres */
    constexpr Length operator"" _km(long double value) { return static_cast<float>(value)* kilometre; }
    /**< Defines the literal of kilometres */
    constexpr Length operator"" _km(unsigned long long int value) { return static_cast<float>(value)* kilometre; }
    /**< Defines the literal of nautical miles */
    constexpr Length operator"" _nm(long double value) { return static_cast<float>(value)* nauticmile; }
    /**< Defines the literal of nautical miles */
    constexpr Length operator"" _nm(unsigned long long int value) { return static_cast<float>(value)* nauticmile; }

    /**< Defines a second */
    constexpr Time second(1.0f);
    /**< Defines a millisecond */
    constexpr Time millisecond = second / 1000.0f;
    /**< Defines a minute */
    constexpr Time minute = 60.0f * second;
    /**< Defines a hour */
    constexpr Time hour = 60.0f * minute;
    /**< Defines the literal of milliseconds */
    constexpr Time operator"" _ms(long double value) { return static_cast<float>(value) * millisecond; }
    /**< Defines the literal of milliseconds */
    constexpr Time operator"" _ms(unsigned long long int value) { return static_cast<float>(value) * millisecond; }
    /**< Defines the literal of seconds */
    constexpr Time operator"" _s(long double value) { return static_cast<float>(value) * second; }
    /**< Defines the literal of seconds */
    constexpr Time operator"" _s(unsigned long long int value) { return static_cast<float>(value) * second; }
    /**< Defines the literal of minutes */
    constexpr Time operator"" _min(long double value) { return static_cast<float>(value) * minute; }
    /**< Defines the literal of minutes */
    constexpr Time operator"" _min(unsigned long long int value) { return static_cast<float>(value) * minute; }
    /**< Defines the literal of hours */
    constexpr Time operator"" _h(long double value) { return static_cast<float>(value) * hour; }
    /**< Defines the literal of hours */
    constexpr Time operator"" _h(unsigned long long int value) { return static_cast<float>(value) * hour; }

    /**< Defines the literal of PI */
    constexpr float operator"" _pi(long double value) { return static_cast<float>(value) * 3.1415926535897932384626433832795f; }
    /**< Defines the literal of PI */
    constexpr float operator"" _pi(unsigned long long int value) { return static_cast<float>(value) * 3.1415926535897932384626433832795f; }
    /**< Defines a degree */
    constexpr Angle degree = Angle(1.0f);
    /**< Defines a radian */
    constexpr Angle radian = 180.0f / 1_pi * degree;
    /**< Defines the literal of radians */
    constexpr Angle operator"" _rad(long double value) { return static_cast<float>(value) * radian; }
    /**< Defines the literal of radians */
    constexpr Angle operator"" _rad(unsigned long long int value) { return static_cast<float>(value) * radian; }
    /**< Defines the literal of degrees */
    constexpr Angle operator"" _deg(long double value) { return static_cast<float>(value) * degree; }
    /**< Defines the literal of degrees */
    constexpr Angle operator"" _deg(unsigned long long int value) { return static_cast<float>(value) * degree; }

    /**< Defines a knot */
    constexpr Velocity knot = 0.51444f * metre / second;
    /**< Defines the literal of metre per second */
    constexpr Velocity operator"" _mps(long double value) { return Velocity(static_cast<float>(value)); }
    /**< Defines the literal of metre per second */
    constexpr Velocity operator"" _mps(unsigned long long int value) { return Velocity(static_cast<float>(value)); }
    /**< Defines the literal of feet per minute */
    constexpr Velocity operator"" _ftpmin(long double value) { return static_cast<float>(value) * feet / minute; }
    /**< Defines the literal of feet per minute */
    constexpr Velocity operator"" _ftpmin(unsigned long long int value) { return static_cast<float>(value) * feet / minute; }
    /**< Defines the literal of kilometre per hour */
    constexpr Velocity operator"" _kmph(long double value) { return static_cast<float>(value) * kilometre / hour; }
    /**< Defines the literal of kilometre per hour */
    constexpr Velocity operator"" _kmph(unsigned long long int value) { return static_cast<float>(value) * kilometre / hour; }
    /**< Defines the literal of knots */
    constexpr Velocity operator"" _kn(long double value) { return static_cast<float>(value) * knot; }
    /**< Defines the literal of knots */
    constexpr Velocity operator"" _kn(unsigned long long int value) { return static_cast<float>(value) * knot; }

    /**< Defines the gravity */
    constexpr Acceleration G = 9.80665f * metre / (second* second);
    /**< Defines the literal of metre per square-second */
    constexpr Acceleration operator"" _mps2(long double value) { return Acceleration(static_cast<float>(value)); }
    /**< Defines the literal of metre per square-second */
    constexpr Acceleration operator"" _mps2(unsigned long long int value) { return Acceleration(static_cast<float>(value)); }
    /**< Defines the literal of gravities */
    constexpr Acceleration operator"" _g(long double value) { return static_cast<float>(value) * G; }
    /**< Defines the literal of gravities */
    constexpr Acceleration operator"" _g(unsigned long long int value) { return static_cast<float>(value) * G; }

    /**< Defines the literal of radian per second */
    constexpr AngularVelocity operator"" _radps(long double value) { return AngularVelocity(static_cast<float>(value)); }
    /**< Defines the literal of radian per second */
    constexpr AngularVelocity operator"" _radps(unsigned long long int value) { return AngularVelocity(static_cast<float>(value)); }
    /**< Defines the literal of degree per second */
    constexpr AngularVelocity operator"" _degps(long double value) { return static_cast<float>(value) * degree / second; }
    /**< Defines the literal of degree per second */
    constexpr AngularVelocity operator"" _degps(unsigned long long int value) { return static_cast<float>(value) * degree / second; }

    /**< Defines the literal of radian per square-second */
    constexpr AngularAcceleration operator"" _radps2(long double value) { return AngularAcceleration(static_cast<float>(value)); }
    /**< Defines the literal of radian per square-second */
    constexpr AngularAcceleration operator"" _radps2(unsigned long long int value) { return AngularAcceleration(static_cast<float>(value)); }
    /**< Defines the literal of degree per square-second */
    constexpr AngularAcceleration operator"" _degps2(long double value) { return static_cast<float>(value) * degree / (second * second); }
    /**< Defines the literal of degree per square-second */
    constexpr AngularAcceleration operator"" _degps2(unsigned long long int value) { return static_cast<float>(value) * degree / (second * second); }
}