internal.h

Go to the documentation of this file.

 
#pragma once
#include <limits>
#include <utility>
#include <algorithm>
#include <cmath>
#define SI_INLINE_CONSTEXPR constexpr inline
 
namespace SI {
    typedef long double angle;      
    typedef angle radians;          
    typedef double SIdouble;        
 
    namespace internal {
        namespace detail {
            template <class T> struct vec_trivally_constructible { using type = T; };
            template <class T> struct vec_value_type { using type = T; };
            template <class T> struct vec_value_type<vec_trivally_constructible<T>> { using type = T; };
            template <class... T> using vec_common_type_t = std::common_type_t<typename vec_value_type<T>::type...>;
        }
 
        template <int N, class T>
        struct vec;
 
        template <class T>
        struct vec<2, T> : vec<2, detail::vec_trivally_constructible<T>> {
            using vec<2, detail::vec_trivally_constructible<T>>::vec;
            SI_INLINE_CONSTEXPR vec() : vec<2, detail::vec_trivally_constructible<T>>(0, 0) {}
        };
 
        template <class T>
        struct vec<2, detail::vec_trivally_constructible<T>> {
            static_assert(std::is_arithmetic_v<T>);
            SI_INLINE_CONSTEXPR vec() = default;
            SI_INLINE_CONSTEXPR vec(T x, T y) : x(x), y(y) {
                static_assert(sizeof(vec) == 2 * sizeof(T));
            }
 
            template <class U>
            SI_INLINE_CONSTEXPR explicit vec(const vec<2, U>& other) : vec(static_cast<T>(other.x), static_cast<T>(other.y)) {}
 
            template <class U>
            SI_INLINE_CONSTEXPR operator vec<2, U>() const { return vec<2, U>(x, static_cast<detail::vec_common_type_t<U>>(y)); } // NOLINT(google-explicit-constructor)
 
            template <class U>
            SI_INLINE_CONSTEXPR explicit vec(const vec<3, U>& other) : vec(static_cast<T>(other.x), static_cast<T>(other.y)) {}
 
            SI_INLINE_CONSTEXPR explicit operator bool() const noexcept { return x != 0 || y != 0; }
 
            T x;
            T y;
        };
 
        template <class T>
        struct vec<3, T> : vec<3, detail::vec_trivally_constructible<T>> {
            using vec<3, detail::vec_trivally_constructible<T>>::vec;
            SI_INLINE_CONSTEXPR vec() : vec<3, detail::vec_trivally_constructible<T>>(0, 0, 0) {}
        };
 
        template <class T>
        struct vec<3, detail::vec_trivally_constructible<T>> {
            static_assert(std::is_arithmetic_v<T>);
            SI_INLINE_CONSTEXPR vec() = default;
            SI_INLINE_CONSTEXPR vec(T x, T y, T z) : x(x), y(y), z(z) {
                static_assert(sizeof(vec) == 3 * sizeof(T));
            }
 
            template <class U>
            SI_INLINE_CONSTEXPR vec(const vec<2, U>& xy, T z) : vec(xy.x, xy.y, z) {}
 
            template <class U>
            SI_INLINE_CONSTEXPR explicit vec(const vec<3, U>& other) : vec(static_cast<T>(other.x), static_cast<T>(other.y), static_cast<T>(other.z)) {}
 
            template <class U>
            SI_INLINE_CONSTEXPR operator vec<3, U>() const { return vec<3, U>(x, static_cast<detail::vec_common_type_t<U>>(y), static_cast<detail::vec_common_type_t<U>>(z)); } // NOLINT(google-explicit-constructor)
 
            SI_INLINE_CONSTEXPR explicit operator bool() const noexcept { return !(x == 0 && y == 0 && z == 0); }
            union {
                struct {
                    T x;
                    T y;
                };
                internal::vec<2, detail::vec_trivally_constructible<T>> xy;
            };
            T z;
        };
 
        template <class T> using vec2 = vec<2, T>;
        template <class T> using vec3 = vec<3, T>;
 
        // unary operators
        template <class T> [[nodiscard]] SI_INLINE_CONSTEXPR vec2<T> operator-(const vec2<T>& v) { return { -v.x, -v.y }; }
        template <class T> [[nodiscard]] SI_INLINE_CONSTEXPR vec3<T> operator-(const vec3<T>& v) { return { -v.x, -v.y, -v.z }; }
 
        // comparsion operators
        template <class T, class U> [[nodiscard]] SI_INLINE_CONSTEXPR bool operator==(const vec2<T>& lhs, const vec2<U>& rhs) { return lhs.x == rhs.x && lhs.y == rhs.y; }
        template <class T, class U> [[nodiscard]] SI_INLINE_CONSTEXPR bool operator==(const vec3<T>& lhs, const vec3<U>& rhs) { return lhs.x == rhs.x && lhs.y == rhs.y && lhs.z == rhs.z; }
        template <class T, class U> [[nodiscard]] SI_INLINE_CONSTEXPR bool operator!=(const vec2<T>& lhs, const vec2<U>& rhs) { return lhs.x != rhs.x || lhs.y != rhs.y; }
        template <class T, class U> [[nodiscard]] SI_INLINE_CONSTEXPR bool operator!=(const vec3<T>& lhs, const vec3<U>& rhs) { return lhs.x != rhs.x || lhs.y != rhs.y || lhs.z != rhs.z; }
 
        // compound assignment with other vectors
        template <class T, class U> SI_INLINE_CONSTEXPR vec2<T>& operator+=(vec2<T>& lhs, const vec2<U>& rhs) { lhs.x += rhs.x; lhs.y += rhs.y; return lhs; }
        template <class T, class U> SI_INLINE_CONSTEXPR vec3<T>& operator+=(vec3<T>& lhs, const vec3<U>& rhs) { lhs.x += rhs.x; lhs.y += rhs.y; lhs.z += rhs.z; return lhs; }
        template <class T, class U> SI_INLINE_CONSTEXPR vec2<T>& operator-=(vec2<T>& lhs, const vec2<U>& rhs) { lhs.x -= rhs.x; lhs.y -= rhs.y; return lhs; }
        template <class T, class U> SI_INLINE_CONSTEXPR vec3<T>& operator-=(vec3<T>& lhs, const vec3<U>& rhs) { lhs.x -= rhs.x; lhs.y -= rhs.y; lhs.z -= rhs.z; return lhs; }
        template <class T, class U> SI_INLINE_CONSTEXPR vec2<T>& operator*=(vec2<T>& lhs, const vec2<U>& rhs) { lhs.x *= rhs.x; lhs.y *= rhs.y; return lhs; }
        template <class T, class U> SI_INLINE_CONSTEXPR vec3<T>& operator*=(vec3<T>& lhs, const vec3<U>& rhs) { lhs.x *= rhs.x; lhs.y *= rhs.y; lhs.z *= rhs.z; return lhs; }
        template <class T, class U> SI_INLINE_CONSTEXPR vec2<T>& operator/=(vec2<T>& lhs, const vec2<U>& rhs) { lhs.x /= rhs.x; lhs.y /= rhs.y; return lhs; }
        template <class T, class U> SI_INLINE_CONSTEXPR vec3<T>& operator/=(vec3<T>& lhs, const vec3<U>& rhs) { lhs.x /= rhs.x; lhs.y /= rhs.y; lhs.z /= rhs.z; return lhs; }
 
        // compound assignment with scalars
        template <class T, class U> SI_INLINE_CONSTEXPR std::enable_if_t<std::is_arithmetic_v<U>, vec2<T>&> operator+=(vec2<T>& lhs, U rhs) { lhs.x += rhs; lhs.y += rhs; return lhs; }
        template <class T, class U> SI_INLINE_CONSTEXPR std::enable_if_t<std::is_arithmetic_v<U>, vec3<T>&> operator+=(vec3<T>& lhs, U rhs) { lhs.x += rhs; lhs.y += rhs; lhs.z += rhs; return lhs; }
        template <class T, class U> SI_INLINE_CONSTEXPR std::enable_if_t<std::is_arithmetic_v<U>, vec2<T>&> operator-=(vec2<T>& lhs, U rhs) { lhs.x -= rhs; lhs.y -= rhs; return lhs; }
        template <class T, class U> SI_INLINE_CONSTEXPR std::enable_if_t<std::is_arithmetic_v<U>, vec3<T>&> operator-=(vec3<T>& lhs, U rhs) { lhs.x -= rhs; lhs.y -= rhs; lhs.z -= rhs; return lhs; }
        template <class T, class U> SI_INLINE_CONSTEXPR std::enable_if_t<std::is_arithmetic_v<U>, vec2<T>&> operator*=(vec2<T>& lhs, U rhs) { lhs.x *= rhs; lhs.y *= rhs; return lhs; }
        template <class T, class U> SI_INLINE_CONSTEXPR std::enable_if_t<std::is_arithmetic_v<U>, vec3<T>&> operator*=(vec3<T>& lhs, U rhs) { lhs.x *= rhs; lhs.y *= rhs; lhs.z *= rhs; return lhs; }
        template <class T, class U> SI_INLINE_CONSTEXPR std::enable_if_t<std::is_arithmetic_v<U>, vec2<T>&> operator/=(vec2<T>& lhs, U rhs) { lhs.x /= rhs; lhs.y /= rhs; return lhs; }
        template <class T, class U> SI_INLINE_CONSTEXPR std::enable_if_t<std::is_arithmetic_v<U>, vec3<T>&> operator/=(vec3<T>& lhs, U rhs) { lhs.x /= rhs; lhs.y /= rhs; lhs.z /= rhs; return lhs; }
 
        // binary operators with other vectors
        template <class T, class U> [[nodiscard]] SI_INLINE_CONSTEXPR vec2<detail::vec_common_type_t<T, U>> operator+(const vec2<T>& lhs, const vec2<U>& rhs) { return {lhs.x + rhs.x, lhs.y + rhs.y }; }
        template <class T, class U> [[nodiscard]] SI_INLINE_CONSTEXPR vec3<detail::vec_common_type_t<T, U>> operator+(const vec3<T>& lhs, const vec3<U>& rhs) { return {lhs.x + rhs.x, lhs.y + rhs.y, lhs.z + rhs.z }; }
        template <class T, class U> [[nodiscard]] SI_INLINE_CONSTEXPR vec2<detail::vec_common_type_t<T, U>> operator-(const vec2<T>& lhs, const vec2<U>& rhs) { return {lhs.x - rhs.x, lhs.y - rhs.y }; }
        template <class T, class U> [[nodiscard]] SI_INLINE_CONSTEXPR vec3<detail::vec_common_type_t<T, U>> operator-(const vec3<T>& lhs, const vec3<U>& rhs) { return {lhs.x - rhs.x, lhs.y - rhs.y, lhs.z - rhs.z }; }
        template <class T, class U> [[nodiscard]] SI_INLINE_CONSTEXPR vec2<detail::vec_common_type_t<T, U>> operator*(const vec2<T>& lhs, const vec2<U>& rhs) { return {lhs.x * rhs.x, lhs.y * rhs.y }; }
        template <class T, class U> [[nodiscard]] SI_INLINE_CONSTEXPR vec3<detail::vec_common_type_t<T, U>> operator*(const vec3<T>& lhs, const vec3<U>& rhs) { return {lhs.x * rhs.x, lhs.y * rhs.y, lhs.z * rhs.z }; }
        template <class T, class U> [[nodiscard]] SI_INLINE_CONSTEXPR vec2<detail::vec_common_type_t<T, U>> operator/(const vec2<T>& lhs, const vec2<U>& rhs) { return {lhs.x / rhs.x, lhs.y / rhs.y }; }
        template <class T, class U> [[nodiscard]] SI_INLINE_CONSTEXPR vec3<detail::vec_common_type_t<T, U>> operator/(const vec3<T>& lhs, const vec3<U>& rhs) { return {lhs.x / rhs.x, lhs.y / rhs.y, lhs.z / rhs.z }; }
 
        // binary operators with scalars on the right side
        template <class T, class U> [[nodiscard]] SI_INLINE_CONSTEXPR vec2<detail::vec_common_type_t<T, U>> operator+(const vec2<T>& lhs, U rhs) { return { lhs.x + rhs, lhs.y + rhs}; }
        template <class T, class U> [[nodiscard]] SI_INLINE_CONSTEXPR vec3<detail::vec_common_type_t<T, U>> operator+(const vec3<T>& lhs, U rhs) { return { lhs.x + rhs, lhs.y + rhs, lhs.z + rhs}; }
        template <class T, class U> [[nodiscard]] SI_INLINE_CONSTEXPR vec2<detail::vec_common_type_t<T, U>> operator-(const vec2<T>& lhs, U rhs) { return { lhs.x - rhs, lhs.y - rhs}; }
        template <class T, class U> [[nodiscard]] SI_INLINE_CONSTEXPR vec3<detail::vec_common_type_t<T, U>> operator-(const vec3<T>& lhs, U rhs) { return { lhs.x - rhs, lhs.y - rhs, lhs.z - rhs}; }
        template <class T, class U> [[nodiscard]] SI_INLINE_CONSTEXPR vec2<detail::vec_common_type_t<T, U>> operator*(const vec2<T>& lhs, U rhs) { return { lhs.x * rhs, lhs.y * rhs}; }
        template <class T, class U> [[nodiscard]] SI_INLINE_CONSTEXPR vec3<detail::vec_common_type_t<T, U>> operator*(const vec3<T>& lhs, U rhs) { return { lhs.x * rhs, lhs.y * rhs, lhs.z * rhs}; }
        template <class T, class U> [[nodiscard]] SI_INLINE_CONSTEXPR vec2<detail::vec_common_type_t<T, U>> operator/(const vec2<T>& lhs, U rhs) { return { lhs.x / rhs, lhs.y / rhs}; }
        template <class T, class U> [[nodiscard]] SI_INLINE_CONSTEXPR vec3<detail::vec_common_type_t<T, U>> operator/(const vec3<T>& lhs, U rhs) { return { lhs.x / rhs, lhs.y / rhs, lhs.z / rhs}; }
 
        // binary operators with scalars on the left side
        template <class T, class U> [[nodiscard]] SI_INLINE_CONSTEXPR vec2<detail::vec_common_type_t<T, U>> operator+(T lhs, const vec2<U>& rhs) { return { lhs + rhs.x, lhs + rhs.y }; }
        template <class T, class U> [[nodiscard]] SI_INLINE_CONSTEXPR vec3<detail::vec_common_type_t<T, U>> operator+(T lhs, const vec3<U>& rhs) { return { lhs + rhs.x, lhs + rhs.y, lhs + rhs.z }; }
        template <class T, class U> [[nodiscard]] SI_INLINE_CONSTEXPR vec2<detail::vec_common_type_t<T, U>> operator-(T lhs, const vec2<U>& rhs) { return { lhs - rhs.x, lhs - rhs.y }; }
        template <class T, class U> [[nodiscard]] SI_INLINE_CONSTEXPR vec3<detail::vec_common_type_t<T, U>> operator-(T lhs, const vec3<U>& rhs) { return { lhs - rhs.x, lhs - rhs.y, lhs - rhs.z }; }
        template <class T, class U> [[nodiscard]] SI_INLINE_CONSTEXPR vec2<detail::vec_common_type_t<T, U>> operator*(T lhs, const vec2<U>& rhs) { return { lhs * rhs.x, lhs * rhs.y }; }
        template <class T, class U> [[nodiscard]] SI_INLINE_CONSTEXPR vec3<detail::vec_common_type_t<T, U>> operator*(T lhs, const vec3<U>& rhs) { return { lhs * rhs.x, lhs * rhs.y, lhs * rhs.z }; }
        template <class T, class U> [[nodiscard]] SI_INLINE_CONSTEXPR vec2<detail::vec_common_type_t<T, U>> operator/(T lhs, const vec2<U>& rhs) { return { lhs / rhs.x, lhs / rhs.y }; }
        template <class T, class U> [[nodiscard]] SI_INLINE_CONSTEXPR vec3<detail::vec_common_type_t<T, U>> operator/(T lhs, const vec3<U>& rhs) { return { lhs / rhs.x, lhs / rhs.y, lhs / rhs.z }; }
 
        // absolute value (componentwise)
        template <class T> [[nodiscard]] SI_INLINE_CONSTEXPR vec2<detail::vec_common_type_t<T>> abs(const vec2<T>& v) { return { std::abs(v.x), std::abs(v.y) }; }
        template <class T> [[nodiscard]] SI_INLINE_CONSTEXPR vec3<detail::vec_common_type_t<T>> abs(const vec3<T>& v) { return { std::abs(v.x), std::abs(v.y), std::abs(v.z) }; }
 
        // sign Of (componentwise)
        template <class T> [[nodiscard]] SI_INLINE_CONSTEXPR std::enable_if_t<std::is_arithmetic_v<T>, T> sign(T x) { return x > 0 ? 1 : x < 0 ? -1 : 0; }
        template <class T> [[nodiscard]] SI_INLINE_CONSTEXPR vec2<detail::vec_common_type_t<T>> sign(const vec2<T>& v) { return { sign(v.x), sign(v.y) }; }
        template <class T> [[nodiscard]] SI_INLINE_CONSTEXPR vec3<detail::vec_common_type_t<T>> sign(const vec3<T>& v) { return { sign(v.x), sign(v.y), sign(v.z) }; }
 
        // min / max (componentwise)
        template <class T, class U> [[nodiscard]] SI_INLINE_CONSTEXPR std::enable_if_t<std::is_arithmetic_v<T> && std::is_arithmetic_v<U>, std::common_type_t<T, U>> min(T lhs, U rhs) { return (rhs < lhs) ? rhs : lhs; }
        template <class T, class U> [[nodiscard]] SI_INLINE_CONSTEXPR std::enable_if_t<std::is_arithmetic_v<T> && std::is_arithmetic_v<U>, std::common_type_t<T, U>> max(T lhs, U rhs) { return (lhs < rhs) ? rhs : lhs; }
        template <class T, class U> [[nodiscard]] SI_INLINE_CONSTEXPR vec2<detail::vec_common_type_t<T, U>> min(const vec2<T>& lhs, const vec2<U>& rhs) { return { min(lhs.x, rhs.x), min(lhs.y, rhs.y) }; }
        template <class T, class U> [[nodiscard]] SI_INLINE_CONSTEXPR vec3<detail::vec_common_type_t<T, U>> min(const vec3<T>& lhs, const vec3<U>& rhs) { return { min(lhs.x, rhs.x), min(lhs.y, rhs.y), min(lhs.z, rhs.z) }; }
        template <class T, class U> [[nodiscard]] SI_INLINE_CONSTEXPR vec2<detail::vec_common_type_t<T, U>> max(const vec2<T>& lhs, const vec2<U>& rhs) { return { max(lhs.x, rhs.x), max(lhs.y, rhs.y) }; }
        template <class T, class U> [[nodiscard]] SI_INLINE_CONSTEXPR vec3<detail::vec_common_type_t<T, U>> max(const vec3<T>& lhs, const vec3<U>& rhs) { return { max(lhs.x, rhs.x), max(lhs.y, rhs.y), max(lhs.z, rhs.z) }; }
 
        // clamping (componentwise)
        template <class T, class U, class V> [[nodiscard]] SI_INLINE_CONSTEXPR std::enable_if_t<std::is_arithmetic_v<T>, std::common_type_t<T, U, V>> clamp(T value, U min, V max) { return (min > value) ? min : (max < value) ? max : value; }
        template <class T, class U, class V> [[nodiscard]] SI_INLINE_CONSTEXPR vec2<detail::vec_common_type_t<T, U, V>> clamp(const vec2<T>& value, U min, V max) { return { clamp(value.x, min, max), clamp(value.y, min, max) }; }
        template <class T, class U, class V> [[nodiscard]] SI_INLINE_CONSTEXPR vec2<detail::vec_common_type_t<T, U, V>> clamp(const vec2<T>& value, const vec2<U>& min, const vec2<V>& max) { return { clamp(value.x, min.x, max.x), clamp(value.y, min.y, max.y) }; }
        template <class T, class U, class V> [[nodiscard]] SI_INLINE_CONSTEXPR vec3<detail::vec_common_type_t<T, U, V>> clamp(const vec3<T>& value, U min, V max) { return { clamp(value.x, min, max), clamp(value.y, min, max), clamp(value.z, min, max) }; }
        template <class T, class U, class V> [[nodiscard]] SI_INLINE_CONSTEXPR vec3<detail::vec_common_type_t<T, U, V>> clamp(const vec3<T>& value, const vec3<U>& min, const vec3<V>& max) { return { clamp(value.x, min.x, max.x), clamp(value.y, min.y, max.y), clamp(value.z, min.z, max.z) }; }
 
        // dot product / inner product of two vectors
        template <class T, class U> [[nodiscard]] SI_INLINE_CONSTEXPR auto dot(const vec2<T>& lhs, const vec2<U>& rhs) { return lhs.x * rhs.x + lhs.y * rhs.y; }
        template <class T, class U> [[nodiscard]] SI_INLINE_CONSTEXPR auto dot(const vec3<T>& lhs, const vec3<U>& rhs) { return lhs.x * rhs.x + lhs.y * rhs.y + lhs.z * rhs.z; }
 
        // Euclidean length of a vector
        template <class T> [[nodiscard]] inline auto length(const vec2<T>& v) { return std::sqrt(dot(v, v)); }
        template <class T> [[nodiscard]] inline auto length(const vec3<T>& v) { return std::sqrt(dot(v, v)); }
 
        // normalization (returns null vector when given null vectors for robustness)
        // multiplies with the inverse sqrt to be 1:1 compatible to GLM (avoids minimal, but noticeable deviations)
        template <class T> [[nodiscard]] inline auto normalize(const vec2<T>& v) { auto l = length(v); return v * (l ? (1 / l) : 0); }
        template <class T> [[nodiscard]] inline auto normalize(const vec3<T>& v) { auto l = length(v); return v * (l ? (1 / l) : 0); }
 
        // Euclidean distance between to vectors / points
        template <class T, class U> [[nodiscard]] inline auto distance(const vec2<T>& a, const vec2<U>& b) { return length(b - a); }
        template <class T, class U> [[nodiscard]] inline auto distance(const vec3<T>& a, const vec3<U>& b) { return length(b - a); }
 
        // cross product / outer product of two vectors
        template <class T, class U> [[nodiscard]] SI_INLINE_CONSTEXPR vec3<detail::vec_common_type_t<T, U>> cross(const vec3<T>& lhs, const vec3<U>& rhs) { return { lhs.y * rhs.z - rhs.y * lhs.z, lhs.z * rhs.x - rhs.z * lhs.x, lhs.x * rhs.y - rhs.x * lhs.y }; }
 
        // mixing / interpolation (componentwise), returns `(1 - t) * a + t * b`
        template <class T, class U, class V> [[nodiscard]] SI_INLINE_CONSTEXPR std::common_type_t<T, U, V> mix(T a, U b, V t) { return (1 - t) * a + t * b; }
        template <class T, class U, class V> [[nodiscard]] SI_INLINE_CONSTEXPR vec2<detail::vec_common_type_t<T, U, V>> mix(const vec2<T>& a, const vec2<U>& b, V t) { return { mix(a.x, b.x, t), mix(a.y, b.y, t) }; }
        template <class T, class U, class V> [[nodiscard]] SI_INLINE_CONSTEXPR vec3<detail::vec_common_type_t<T, U, V>> mix(const vec3<T>& a, const vec3<U>& b, V t) { return { mix(a.x, b.x, t), mix(a.y, b.y, t), mix(a.z, b.z, t) }; }
    }
 
    namespace detail {
        template <class T>
        using vec2 = internal::vec2<T>;
 
        template <class T>
        using vec3 = internal::vec3<T>;
 
        // the dimension(s) of a physical quantity, specified by it's dimensional exponents.
        template <long lengthExp, long massExp, long timeExp, long temperatureExp, long currentExp, long substanceExp, long intensityExp>
        struct dimension {
            static constexpr long length = lengthExp;
            static constexpr long mass = massExp;
            static constexpr long time = timeExp;
            static constexpr long temperature = temperatureExp;
            static constexpr long current = currentExp;
            static constexpr long substance = substanceExp;
            static constexpr long intensity = intensityExp;
        };
 
        template <long Value>
        using value_dimension = dimension<Value, Value, Value, Value, Value, Value, Value>;
 
        // the 'dimensionless' datatype with zero dimensions.
        using dimensionless = value_dimension<0>;
 
        template <class, class>
        struct quantity;
        template <class, class>
        struct unit;
 
        template <class T>
        struct dimension_of {
            using type = dimensionless;
        };
 
        template <long Length, long Mass, long Time, long Temperature, long Current, long Substance, long Intensity>
        struct dimension_of<dimension<Length, Mass, Time, Temperature, Current, Substance, Intensity>> {
            using type = dimension<Length, Mass, Time, Temperature, Current, Substance, Intensity>;
        };
 
        template <class Dimension, class T>
        struct dimension_of<quantity<Dimension, T>> {
            using type = Dimension;
        };
 
        template <class Dimension, class Ratio>
        struct dimension_of<unit<Dimension, Ratio>> {
            using type = Dimension;
        };
 
        // Resolves to the dimension of anything that might have a dimension (types with no dimension end up with dimensionless)
        template <class T>
        using dimension_of_t = typename dimension_of<std::decay_t<T>>::type;
 
        // Checks whether the given type is/has dimensionless
        template <class T>
        SI_INLINE_CONSTEXPR bool is_dimensionless_v = std::is_same_v<dimensionless, dimension_of_t<T>>;
 
#define SI_DIMENSION_OP(op_) dimension<                        \
            Lhs::length op_ Rhs::length,           \
            Lhs::mass op_ Rhs::mass,               \
            Lhs::time op_ Rhs::time,               \
            Lhs::temperature op_ Rhs::temperature, \
            Lhs::current op_ Rhs::current,         \
            Lhs::substance op_ Rhs::substance,     \
            Lhs::intensity op_ Rhs::intensity>
 
        template <class Lhs, class Rhs> using dimension_add_impl = SI_DIMENSION_OP(+);
        template <class Lhs, class Rhs> using dimension_subtract_impl = SI_DIMENSION_OP(-);
        template <class Lhs, class Rhs> using dimension_multiply_impl = SI_DIMENSION_OP(*);
        template <class Lhs, class Rhs> using dimension_divide_impl = SI_DIMENSION_OP(/);
        template <class Lhs, class Rhs> using dimension_add = dimension_add_impl <dimension_of_t<Lhs>, dimension_of_t<Rhs>>;
        template <class Lhs, class Rhs> using dimension_subtract = dimension_subtract_impl <dimension_of_t<Lhs>, dimension_of_t<Rhs>>;
        template <class Lhs, class Rhs> using dimension_multiply = dimension_multiply_impl <dimension_of_t<Lhs>, dimension_of_t<Rhs>>;
        template <class Lhs, class Rhs> using dimension_divide = dimension_divide_impl <dimension_of_t<Lhs>, dimension_of_t<Rhs>>;
 
#undef SI_DIMENSION_OP
 
        struct zero_t {};
 
        template <class T> struct scalar_value_type { using type = T; };
        template <> struct scalar_value_type<zero_t> { using type = int; };
        template <class Dimension, class T> struct scalar_value_type<quantity<Dimension, T>> { using type = typename scalar_value_type<T>::type; };
 
        template <class T>
        using scalar_value_type_t = typename scalar_value_type<T>::type;
 
        // Storage for plain arithmetic types (float, double, int, ...)
        template <class Dimension, class T>
        class quantity_storage {
        public:
            SI_INLINE_CONSTEXPR quantity_storage()
                : m_value(0)
            {}
 
            SI_INLINE_CONSTEXPR explicit operator bool() const {
                return static_cast<bool>(m_value);
            }
 
        private:
            T m_value;
 
            friend SI_INLINE_CONSTEXPR const T& value(const quantity_storage& x) {
                return x.m_value;
            }
 
            friend SI_INLINE_CONSTEXPR T& value(quantity_storage& x) {
                return x.m_value;
            }
        };
 
        // Helper function for filling all components of either a scalar or a vector to a given value
        template <class T>
        SI_INLINE_CONSTEXPR std::enable_if_t<std::is_arithmetic_v<T>> fill(T& x, T value) {
            x = value;
        }
 
        template <class Dimension, class T>
        struct quantity final : quantity_storage<Dimension, T>
        {
            static_assert(!is_dimensionless_v<Dimension>); // make sure we are not creating quantities with dimensionless (dimensionlesss should be plain arithmetic types)
            using value_type = T;
            using dimension_type = Dimension;
 
            SI_INLINE_CONSTEXPR quantity(zero_t = {}) { }
 
            SI_INLINE_CONSTEXPR quantity(Dimension, const T& x) {
                value(*this) = x;
            }
 
            template <class U>
            SI_INLINE_CONSTEXPR quantity(const quantity<Dimension, U>& q) {
                value(*this) = value(q);
            }
 
            static SI_INLINE_CONSTEXPR quantity<Dimension, T> infinity() {
                using scalar_type = scalar_value_type_t<T>;
                static_assert(std::is_floating_point_v<scalar_type>);
                T value = {};
                fill(value, std::numeric_limits<scalar_type>::infinity());
                return { Dimension(), value };
            }
 
            static SI_INLINE_CONSTEXPR quantity<Dimension, T> NaN() {
                using scalar_type = scalar_value_type_t<T>;
                static_assert(std::is_floating_point_v<scalar_type>);
                T value = {};
                fill(value, std::numeric_limits<scalar_type>::quiet_NaN());
                return { Dimension(), value };
            }
        };
 
        template <class T>
        struct is_si : std::bool_constant<false> {};
 
        template <class Dimension, class T>
        struct is_si<quantity<Dimension, T> > : std::bool_constant<true> {};
 
        template <>
        struct is_si<zero_t> : std::bool_constant<true> {};
 
        // Checks wheter the given type is a SI type
        template <class T>
        SI_INLINE_CONSTEXPR bool is_si_v = is_si<T>::value;
 
        // Fallback value for any plain type, simply returns the value as-is
        template <class T, class = std::enable_if_t<!is_si_v<T>>>
        SI_INLINE_CONSTEXPR const T& value(const T& x) { return x; }
 
        SI_INLINE_CONSTEXPR long value(zero_t) { return 0; }
 
        // Helper function for arithmetic functions with two arguments, returns the value of the first argument but uses
        // the second argument to deduce the returned type in case of si::zero
        template <class T, class U>
        SI_INLINE_CONSTEXPR decltype(auto) value2(T&& x, U) { return value(std::forward<T>(x)); }
 
        template <class U>
        SI_INLINE_CONSTEXPR auto value2(zero_t, const U& other) {
            // Return zero of the given other type (i.e. return vec2() instead of plain 0)
            return decltype(value(other)){};
        }
 
        // Checks wheter two types have compatible dimensions (zero is compatible with everything)
        template <class Lhs, class Rhs>
        SI_INLINE_CONSTEXPR bool has_common_dimension_v = std::is_same_v<dimension_of_t<Lhs>, dimension_of_t<Rhs>> || std::is_same_v<Lhs, zero_t> || std::is_same_v<Rhs, zero_t>;
 
        template <class Lhs, class Rhs>
        using dimension_common = std::conditional_t<std::is_same_v<Lhs, zero_t>, dimension_of_t<Rhs>, dimension_of_t<Lhs>>;
 
        template <class T, class U = void, class V = void>
        using enable_for_si = std::enable_if_t<is_si_v<T> || is_si_v<U> || is_si_v<V>>;
 
        template <class T, class Dimension>
        SI_INLINE_CONSTEXPR quantity<Dimension, T> operator-(quantity<Dimension, T> x) {
            value(x) = -value(x);
            return x;
        }
 
        template <class T, class Dimension, class U>
        SI_INLINE_CONSTEXPR quantity<Dimension, T>& operator+=(quantity<Dimension, T>& lhs, const U& rhs) {
            static_assert(has_common_dimension_v<Dimension, U>, "incompatible SI dimensions");
            value(lhs) += value(rhs);
            return lhs;
        }
 
        template <class T, class Dimension, class U>
        SI_INLINE_CONSTEXPR quantity<Dimension, T>& operator-=(quantity<Dimension, T>& lhs, const U& rhs) {
            static_assert(has_common_dimension_v<Dimension, U>, "incompatible SI dimensions");
            value(lhs) -= value(rhs);
            return lhs;
        }
 
        template <class T, class Dimension, class U>
        SI_INLINE_CONSTEXPR quantity<Dimension, T>& operator*=(quantity<Dimension, T>& lhs, const U& rhs) {
            static_assert(is_dimensionless_v<U>, "incompatible SI dimensions");
            value(lhs) *= value(rhs);
            return lhs;
        }
 
        template <class T, class Dimension, class U>
        SI_INLINE_CONSTEXPR quantity<Dimension, T>& operator/=(quantity<Dimension, T>& lhs, const U& rhs) {
            static_assert(is_dimensionless_v<U>, "incompatible SI dimensions");
            value(lhs) /= value(rhs);
            return lhs;
        }
 
        template <class Lhs, class Rhs, class = enable_for_si<Lhs, Rhs>>
        SI_INLINE_CONSTEXPR auto operator<(const Lhs& lhs, const Rhs& rhs) {
            static_assert(has_common_dimension_v<Lhs, Rhs>, "incompatible SI dimensions");
            return value2(lhs, rhs) < value2(rhs, lhs);
        }
 
        template <class Lhs, class Rhs, class = enable_for_si<Lhs, Rhs>>
        SI_INLINE_CONSTEXPR auto operator<=(const Lhs& lhs, const Rhs& rhs) {
            static_assert(has_common_dimension_v<Lhs, Rhs>, "incompatible SI dimensions");
            return value2(lhs, rhs) <= value2(rhs, lhs);
        }
 
        template <class Lhs, class Rhs, class = enable_for_si<Lhs, Rhs>>
        SI_INLINE_CONSTEXPR auto operator>(const Lhs& lhs, const Rhs& rhs) {
            static_assert(has_common_dimension_v<Lhs, Rhs>, "incompatible SI dimensions");
            return value2(lhs, rhs) > value2(rhs, lhs);
        }
 
        template <class Lhs, class Rhs, class = enable_for_si<Lhs, Rhs>>
        SI_INLINE_CONSTEXPR auto operator>=(const Lhs& lhs, const Rhs& rhs) {
            static_assert(has_common_dimension_v<Lhs, Rhs>, "incompatible SI dimensions");
            return value2(lhs, rhs) >= value2(rhs, lhs);
        }
 
        template <class Lhs, class Rhs, class = enable_for_si<Lhs, Rhs>>
        SI_INLINE_CONSTEXPR auto operator==(const Lhs& lhs, const Rhs& rhs) {
            static_assert(has_common_dimension_v<Lhs, Rhs>, "incompatible SI dimensions");
            return value2(lhs, rhs) == value2(rhs, lhs);
        }
 
        template <class Lhs, class Rhs, class = enable_for_si<Lhs, Rhs>>
        SI_INLINE_CONSTEXPR auto operator!=(const Lhs& lhs, const Rhs& rhs) {
            static_assert(has_common_dimension_v<Lhs, Rhs>, "incompatible SI dimensions");
            return value2(lhs, rhs) != value2(rhs, lhs);
        }
 
        // helper macro returning a quantity for non-null dimensions and plain value otherwise
#define SI_RETURN_QUANTITY(dimension_, ...)                                        \
        if constexpr(is_dimensionless_v<dimension_>) return (__VA_ARGS__); \
        else return quantity{dimension_(), (__VA_ARGS__)}
 
        template <class Lhs, class Rhs, class = enable_for_si<Lhs, Rhs>>
        SI_INLINE_CONSTEXPR auto operator+(const Lhs& lhs, const Rhs& rhs) {
            static_assert(has_common_dimension_v<Lhs, Rhs>, "incompatible SI dimensions");
            using result_dimension = dimension_common<Lhs, Rhs>;
            SI_RETURN_QUANTITY(result_dimension, value2(lhs, rhs) + value2(rhs, lhs));
        }
 
        template <class Lhs, class Rhs, class = enable_for_si<Lhs, Rhs>>
        SI_INLINE_CONSTEXPR auto operator-(const Lhs& lhs, const Rhs& rhs) {
            static_assert(has_common_dimension_v<Lhs, Rhs>, "incompatible SI dimensions");
            using result_dimension = dimension_common<Lhs, Rhs>;
            SI_RETURN_QUANTITY(result_dimension, value2(lhs, rhs) - value2(rhs, lhs));
        }
 
        template <class Lhs, class Rhs, class = enable_for_si<Lhs, Rhs>>
        SI_INLINE_CONSTEXPR auto operator*(const Lhs& lhs, const Rhs& rhs) {
            using result_dimension = dimension_add<Lhs, Rhs>;
            SI_RETURN_QUANTITY(result_dimension, value2(lhs, rhs) * value2(rhs, lhs));
        }
 
        template <class Lhs, class Rhs, class = enable_for_si<Lhs, Rhs>>
        SI_INLINE_CONSTEXPR auto operator/(const Lhs& lhs, const Rhs& rhs) {
            using result_dimension = dimension_subtract<Lhs, Rhs>;
            SI_RETURN_QUANTITY(result_dimension, value2(lhs, rhs) / value2(rhs, lhs));
        }
 
        // Computes the absolute value of x.
        template <class Dimension, class T>
        SI_INLINE_CONSTEXPR quantity<Dimension, T> abs(const quantity<Dimension, T>& x) {
            return value(x) < 0.0 ? -x : x;
        }
 
        template <class Lhs, class Rhs, class = enable_for_si<Lhs, Rhs>>
        SI_INLINE_CONSTEXPR auto dot(const Lhs& lhs, const Rhs& rhs) {
            using result_dimension = dimension_add<Lhs, Rhs>;
            SI_RETURN_QUANTITY(result_dimension, dot(value(lhs), value(rhs)));
        }
 
        template <class Dimension, class T>
        inline auto normalize(const quantity<Dimension, T>& x) {
            return normalize(value(x));
        }
 
        template <class Dimension, class T>
        inline auto norm(const quantity<Dimension, T>& x) {
            return quantity{ Dimension(), length(value(x)) };
        }
 
        template <class T>
        inline auto distance(const quantity<dimension<1, 0, 0, 0, 0, 0, 0>, T>& a, const quantity<dimension<1, 0, 0, 0, 0, 0, 0>, T>& b) {
            return quantity{ dimension<1, 0, 0, 0, 0, 0, 0>(), distance(value(a), value(b)) };
        }
 
        template <long Exponent, class Dimension, class T>
        inline auto pow(const quantity<Dimension, T>& x) {
            using std::pow;
            using result_dimension = dimension_multiply<Dimension, value_dimension<Exponent>>;
            SI_RETURN_QUANTITY(result_dimension, pow(value(x), Exponent));
        }
 
        template <long Degree, class Dimension, class T>
        inline auto root(const quantity<Dimension, T>& x) {
            using std::pow;
            using result_dimension = dimension_divide<Dimension, value_dimension<Degree>>;
            static_assert(std::is_same_v<dimension_multiply<result_dimension, value_dimension<Degree>>, Dimension>, "cannot take root of this SI dimension");
            SI_RETURN_QUANTITY(result_dimension, pow(value(x), 1. / Degree));
        }
 
        template <class Dimension, class T>
        inline auto sqrt(const quantity<Dimension, T>& x) {
            using std::sqrt;
            using result_dimension = dimension_divide<Dimension, value_dimension<2>>;
            static_assert(std::is_same_v<dimension_multiply<result_dimension, value_dimension<2>>, Dimension>, "cannot take sqrt of this SI dimension");
            SI_RETURN_QUANTITY(result_dimension, sqrt(value(x)));
        }
 
        template <class Dimension, class T>
        SI_INLINE_CONSTEXPR auto deangle(const quantity<Dimension, T>& x) {
            using result_dimension = dimension<Dimension::length, Dimension::mass, Dimension::time, Dimension::temperature, Dimension::current, Dimension::substance, Dimension::intensity>;
            SI_RETURN_QUANTITY(result_dimension, value(x));
        }
 
        template <class T> struct element_count : std::integral_constant<int, 1> {};
        template <class Dimension, class T> struct element_count<quantity<Dimension, T>> : element_count<T> {};
 
        template <class T>
        SI_INLINE_CONSTEXPR long element_count_v = element_count<T>::value;
 
        template <class Value, class Min, class Max>
        SI_INLINE_CONSTEXPR auto clamp(const Value& x, const Min& min, const Max& max) {
            static_assert(has_common_dimension_v<Value, Min>, "incompatible SI dimensions");
            static_assert(has_common_dimension_v<Value, Max>, "incompatible SI dimensions");
            using result_dimension = dimension_of_t<Value>;
            SI_RETURN_QUANTITY(result_dimension, std::clamp(value(x), value(min), value(max)));
        }
 
        template <long Num, long Den>
        struct ratio {
            static constexpr auto factor = static_cast<SIdouble>(Num) / Den;
        };
 
        struct tag_celsius {};
        struct tag_fahrenheit {};
 
        template <class Lhs, class Rhs>
        struct ratio_product {
            static constexpr auto factor = Lhs::factor * Rhs::factor;
        };
 
        template <class Lhs, class Rhs>
        struct ratio_quotient {
            static constexpr auto factor = Lhs::factor / Rhs::factor;
        };
 
        template <class T>
        using promoted_scalar_type = std::conditional_t<std::is_same_v<scalar_value_type_t<T>, SIdouble>, SIdouble, SIdouble>;
 
        template <class T>
        struct is_arithmetic : std::is_arithmetic<T> {};
 
        template <class Dimension, class UnitRatio>
        struct unit {
            template <class T, class = std::enable_if_t<is_arithmetic<T>::value>>
            SI_INLINE_CONSTEXPR auto operator()(const T& x) const {
                using scalar_type = promoted_scalar_type<T>;
                if constexpr (std::is_same_v<tag_celsius, UnitRatio>) {
                    SI_RETURN_QUANTITY(Dimension, x + static_cast<scalar_type>(273.15));
                }
                else if constexpr (std::is_same_v<tag_fahrenheit, UnitRatio>) {
                    SI_RETURN_QUANTITY(Dimension, (x + static_cast<scalar_type>(459.67)) * static_cast<scalar_type>(5. / 9));
                }
                else {
                    SI_RETURN_QUANTITY(Dimension, x * static_cast<scalar_type>(UnitRatio::factor));
                }
            }
            template <class T, class U>
            SI_INLINE_CONSTEXPR auto operator()(T x, U y) const {
                using common_type = std::common_type_t<T, U>;
                using scalar_type = promoted_scalar_type<common_type>;
 
                if constexpr (std::is_same_v<tag_celsius, UnitRatio>) {
                    SI_RETURN_QUANTITY(Dimension, vec2<scalar_type>(x, y) + static_cast<scalar_type>(273.15));
                }
                else if constexpr (std::is_same_v<tag_fahrenheit, UnitRatio>) {
                    SI_RETURN_QUANTITY(Dimension, (vec2<scalar_type>(x, y) + static_cast<scalar_type>(459.67)) * static_cast<scalar_type>(5. / 9));
                }
                else {
                    SI_RETURN_QUANTITY(Dimension, vec2<scalar_type>(x, y) * static_cast<scalar_type>(UnitRatio::factor));
                }
            }
 
            template <class T, class U, class V>
            SI_INLINE_CONSTEXPR auto operator()(T x, U y, V z) const {
                using common_type = std::common_type_t<T, U, V>;
                using scalar_type = promoted_scalar_type<common_type>;
 
                if constexpr (std::is_same_v<tag_celsius, UnitRatio>) {
                    SI_RETURN_QUANTITY(Dimension, vec3<scalar_type>(x, y, z) + static_cast<scalar_type>(273.15));
                }
                else if constexpr (std::is_same_v<tag_fahrenheit, UnitRatio>) {
                    SI_RETURN_QUANTITY(Dimension, (vec3<scalar_type>(x, y, z) + static_cast<scalar_type>(459.67)) * static_cast<scalar_type>(5. / 9));
                }
                else
                {
                    SI_RETURN_QUANTITY(Dimension, vec3<scalar_type>(x, y, z) * static_cast<scalar_type>(UnitRatio::factor));
                }
            }
 
            template <class T>
            SI_INLINE_CONSTEXPR auto operator()(const quantity<Dimension, T>& q) const {
                using scalar_type = promoted_scalar_type<T>;
 
                if constexpr(std::is_same_v<tag_celsius, UnitRatio>)
                    return value(q) - static_cast<scalar_type>(273.15);
                else if constexpr (std::is_same_v<tag_fahrenheit, UnitRatio>)
                    return value(q) * static_cast<scalar_type>(9. / 5) - static_cast<scalar_type>(459.67);
                else
                    return value(q) / static_cast<scalar_type>(UnitRatio::factor);
            }
        };
 
        template <class Dimension, long N>
        struct unit<Dimension, ratio<N, N>> {
            template <class T, class = std::enable_if_t<is_arithmetic<T>::value>>
            SI_INLINE_CONSTEXPR auto operator()(T value) const {
                SI_RETURN_QUANTITY(Dimension, value);
            }
 
            // Special operator for constructing a SI quantity from a trivally constructible internal::vec
            template <long D, class T>
            SI_INLINE_CONSTEXPR auto operator()(const internal::vec<D, internal::detail::vec_trivally_constructible<T>>& value) const {
                SI_RETURN_QUANTITY(Dimension, internal::vec<D, T>(value));
            }
 
            template <class T, class U>
            SI_INLINE_CONSTEXPR auto operator()(T x, U y) const {
                using common_type = std::common_type_t<T, U>;
                SI_RETURN_QUANTITY(Dimension, vec2<common_type>(x, y));
            }
 
            template <class T, class U, class V>
            SI_INLINE_CONSTEXPR auto operator()(T x, U y, V z) const {
                using common_type = std::common_type_t<T, U, V>;
                SI_RETURN_QUANTITY(Dimension, vec3<common_type>(x, y, z));
            }
 
            template <class T>
            SI_INLINE_CONSTEXPR T operator()(const quantity<Dimension, T>& q) const {
                return value(q);
            }
 
            SI_INLINE_CONSTEXPR SIdouble operator()(const quantity<Dimension, SIdouble>& q) const {
                return value(q);
            }
 
            SI_INLINE_CONSTEXPR vec2<SIdouble> operator()(const quantity<Dimension, vec2<SIdouble>>& q) const {
                return value(q);
            }
 
            SI_INLINE_CONSTEXPR vec3<SIdouble> operator()(const quantity<Dimension, vec3<SIdouble>>& q) const {
                return value(q);
            }
        };
 
        template <class Ratio>
        struct unit<dimensionless, Ratio> {};
 
        template <long N>
        struct unit<dimensionless, ratio<N, N>> {
            template <class T, class = std::enable_if_t<is_arithmetic<T>::value>>
            SI_INLINE_CONSTEXPR const T& operator()(const T& value) const {
                return value;
            }
        };
 
        template <class DimensionLhs, class RatioLhs, class DimensionRhs, class RatioRhs>
        SI_INLINE_CONSTEXPR auto operator*(unit<DimensionLhs, RatioLhs>, unit<DimensionRhs, RatioRhs>) {
            return unit<dimension_add<DimensionLhs, DimensionRhs>, ratio_product<RatioLhs, RatioRhs>>();
        }
 
        template <class DimensionLhs, class RatioLhs, class DimensionRhs, class RatioRhs>
        SI_INLINE_CONSTEXPR auto operator/(unit<DimensionLhs, RatioLhs>, unit<DimensionRhs, RatioRhs>) {
            return unit<dimension_subtract<DimensionLhs, DimensionRhs>, ratio_quotient<RatioLhs, RatioRhs>>();
        }
    }
 
    SI_INLINE_CONSTEXPR detail::zero_t zero;
 
    template <class Dimension, long long numerator = 1, long long denumerator = 1>
    using unit = detail::unit<detail::dimension_of_t<Dimension>, detail::ratio<numerator, denumerator>>;
 
    using detail::abs;
    using detail::normalize;
    using detail::norm;
    using detail::distance;
    using detail::pow;
    using detail::root;
    using detail::sqrt;
    using detail::dot;
    using detail::clamp;
    using detail::deangle;
    using detail::is_si;
    using detail::is_si_v;
} // end of namespace SI