magnum/src/Math/Vector.h

#ifndef Magnum_Math_Vector_h
#define Magnum_Math_Vector_h
/*
    This file is part of Magnum.

    Copyright © 2010, 2011, 2012, 2013 Vladimír Vondruš <mosra@centrum.cz>

    Permission is hereby granted, free of charge, to any person obtaining a
    copy of this software and associated documentation files (the "Software"),
    to deal in the Software without restriction, including without limitation
    the rights to use, copy, modify, merge, publish, distribute, sublicense,
    and/or sell copies of the Software, and to permit persons to whom the
    Software is furnished to do so, subject to the following conditions:

    The above copyright notice and this permission notice shall be included
    in all copies or substantial portions of the Software.

    THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
    IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
    FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
    THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
    LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
    FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
    DEALINGS IN THE SOFTWARE.
*/

/** @file
 * @brief Class Magnum::Math::Vector
 */

#include <cmath>
#include <limits>
#include <Utility/Assert.h>
#include <Utility/Debug.h>
#include <Utility/ConfigurationValue.h>

#include "Math/Angle.h"
#include "Math/BoolVector.h"
#include "Math/TypeTraits.h"

#include "magnumVisibility.h"

namespace Magnum { namespace Math {

#ifndef DOXYGEN_GENERATING_OUTPUT
namespace Implementation {
    template<std::size_t, class, class> struct VectorConverter;
}
#endif

/**
@brief %Vector
@tparam size    %Vector size
@tparam T       Underlying data type

See @ref matrix-vector for brief introduction.
@configurationvalueref{Magnum::Math::Vector}
*/
template<std::size_t size, class T> class Vector {
    static_assert(size != 0, "Vector cannot have zero elements");

    template<std::size_t, class> friend class Vector;

    public:
        typedef T Type;                         /**< @brief Underlying data type */
        const static std::size_t Size = size;   /**< @brief %Vector size */

        /**
         * @brief %Vector from array
         * @return Reference to the data as if it was Vector, thus doesn't
         *      perform any copying.
         *
         * @attention Use with caution, the function doesn't check whether the
         *      array is long enough.
         */
        inline constexpr static Vector<size, T>& from(T* data) {
            return *reinterpret_cast<Vector<size, T>*>(data);
        }
        /** @overload */
        inline constexpr static const Vector<size, T>& from(const T* data) {
            return *reinterpret_cast<const Vector<size, T>*>(data);
        }

        /**
         * @brief Dot product
         *
         * @f[
         *      \boldsymbol a \cdot \boldsymbol b = \sum_{i=0}^{n-1} \boldsymbol a_i \boldsymbol b_i
         * @f]
         * @see dot() const
         */
        inline static T dot(const Vector<size, T>& a, const Vector<size, T>& b) {
            return (a*b).sum();
        }

        /**
         * @brief Angle between normalized vectors
         *
         * Expects that both vectors are normalized. @f[
         *      \theta = acos \left( \frac{\boldsymbol a \cdot \boldsymbol b}{|\boldsymbol a| |\boldsymbol b|} \right) = acos (\boldsymbol a \cdot \boldsymbol b)
         * @f]
         * @see isNormalized(), Quaternion::angle(), Complex::angle()
         */
        inline static Rad<T> angle(const Vector<size, T>& normalizedA, const Vector<size, T>& normalizedB) {
            CORRADE_ASSERT(normalizedA.isNormalized() && normalizedB.isNormalized(),
                           "Math::Vector::angle(): vectors must be normalized", Rad<T>(std::numeric_limits<T>::quiet_NaN()));
            return Rad<T>(std::acos(dot(normalizedA, normalizedB)));
        }

        /**
         * @brief Default constructor
         *
         * @f[
         *      \boldsymbol v = \boldsymbol 0
         * @f]
         */
        inline constexpr /*implicit*/ Vector(): _data() {}

        /** @todo Creating Vector from combination of vector and scalar types */

        /**
         * @brief Construct vector from values
         * @param first First value
         * @param next  Next values
         */
        #ifdef DOXYGEN_GENERATING_OUTPUT
        template<class ...U> inline constexpr /*implicit*/ Vector(T first, U... next);
        #else
        template<class ...U, class V = typename std::enable_if<sizeof...(U)+1 == size, T>::type> inline constexpr /*implicit*/ Vector(T first, U... next): _data{first, next...} {}
        #endif

        /** @brief Construct vector with one value for all fields */
        #ifdef DOXYGEN_GENERATING_OUTPUT
        inline explicit Vector(T value);
        #else
        #ifndef CORRADE_GCC46_COMPATIBILITY
        template<class U, class V = typename std::enable_if<std::is_same<T, U>::value && size != 1, T>::type> inline constexpr explicit Vector(U value): Vector(typename Implementation::GenerateSequence<size>::Type(), value) {}
        #else
        template<class U, class V = typename std::enable_if<std::is_same<T, U>::value && size != 1, T>::type> inline explicit Vector(U value) {
            *this = Vector(typename Implementation::GenerateSequence<size>::Type(), value);
        }
        #endif
        #endif

        /**
         * @brief Construct vector from another of different type
         *
         * Performs only default casting on the values, no rounding or
         * anything else. Example usage:
         * @code
         * Vector<4, Float> floatingPoint(1.3f, 2.7f, -15.0f, 7.0f);
         * Vector<4, Byte> integral(floatingPoint);
         * // integral == {1, 2, -15, 7}
         * @endcode
         */
        #ifndef CORRADE_GCC46_COMPATIBILITY
        template<class U> inline constexpr explicit Vector(const Vector<size, U>& other): Vector(typename Implementation::GenerateSequence<size>::Type(), other) {}
        #else
        template<class U> inline explicit Vector(const Vector<size, U>& other) {
            *this = Vector(typename Implementation::GenerateSequence<size>::Type(), other);
        }
        #endif

        /** @brief Construct vector from external representation */
        template<class U, class V = decltype(Implementation::VectorConverter<size, T, U>::from(std::declval<U>()))> inline constexpr explicit Vector(const U& other): Vector(Implementation::VectorConverter<size, T, U>::from(other)) {}

        /** @brief Copy constructor */
        inline constexpr Vector(const Vector<size, T>&) = default;

        /** @brief Assignment operator */
        inline Vector<size, T>& operator=(const Vector<size, T>&) = default;

        /** @brief Convert vector to external representation */
        template<class U, class V = decltype(Implementation::VectorConverter<size, T, U>::to(std::declval<Vector<size, T>>()))> inline constexpr explicit operator U() const {
            return Implementation::VectorConverter<size, T, U>::to(*this);
        }

        /**
         * @brief Raw data
         * @return One-dimensional array of `size*size` length.
         *
         * @see operator[]()
         */
        inline T* data() { return _data; }
        inline constexpr const T* data() const { return _data; } /**< @overload */

        /**
         * @brief Value at given position
         *
         * @see data()
         */
        inline T& operator[](std::size_t pos) { return _data[pos]; }
        inline constexpr T operator[](std::size_t pos) const { return _data[pos]; } /**< @overload */

        /** @brief Equality comparison */
        inline bool operator==(const Vector<size, T>& other) const {
            for(std::size_t i = 0; i != size; ++i)
                if(!TypeTraits<T>::equals(_data[i], other._data[i])) return false;

            return true;
        }

        /** @brief Non-equality comparison */
        inline bool operator!=(const Vector<size, T>& other) const {
            return !operator==(other);
        }

        /** @brief Component-wise less than */
        inline BoolVector<size> operator<(const Vector<size, T>& other) const {
            BoolVector<size> out;

            for(std::size_t i = 0; i != size; ++i)
                out.set(i, _data[i] < other._data[i]);

            return out;
        }

        /** @brief Component-wise less than or equal */
        inline BoolVector<size> operator<=(const Vector<size, T>& other) const {
            BoolVector<size> out;

            for(std::size_t i = 0; i != size; ++i)
                out.set(i, _data[i] <= other._data[i]);

            return out;
        }

        /** @brief Component-wise greater than or equal */
        inline BoolVector<size> operator>=(const Vector<size, T>& other) const {
            BoolVector<size> out;

            for(std::size_t i = 0; i != size; ++i)
                out.set(i, _data[i] >= other._data[i]);

            return out;
        }

        /** @brief Component-wise greater than */
        inline BoolVector<size> operator>(const Vector<size, T>& other) const {
            BoolVector<size> out;

            for(std::size_t i = 0; i != size; ++i)
                out.set(i, _data[i] > other._data[i]);

            return out;
        }

        /**
         * @brief Whether the vector is normalized
         *
         * The vector is normalized if it has unit length: @f[
         *      |\boldsymbol a|^2 = |\boldsymbol a| = 1
         * @f]
         * @see dot(), normalized()
         */
        inline bool isNormalized() const {
            return TypeTraits<T>::equals(dot(), T(1));
        }

        /**
         * @brief Negated vector
         *
         * The computation is done in-place. @f[
         *      \boldsymbol a_i = -\boldsymbol a_i
         * @f]
         */
        Vector<size, T> operator-() const {
            Vector<size, T> out;

            for(std::size_t i = 0; i != size; ++i)
                out._data[i] = -_data[i];

            return out;
        }

        /**
         * @brief Add and assign vector
         *
         * The computation is done in-place. @f[
         *      \boldsymbol a_i = \boldsymbol a_i + \boldsymbol b_i
         * @f]
         */
        Vector<size, T>& operator+=(const Vector<size, T>& other) {
            for(std::size_t i = 0; i != size; ++i)
                _data[i] += other._data[i];

            return *this;
        }

        /**
         * @brief Add vector
         *
         * @see operator+=()
         */
        inline Vector<size, T> operator+(const Vector<size, T>& other) const {
            return Vector<size, T>(*this) += other;
        }

        /**
         * @brief Subtract and assign vector
         *
         * The computation is done in-place. @f[
         *      \boldsymbol a_i = \boldsymbol a_i - \boldsymbol b_i
         * @f]
         */
        Vector<size, T>& operator-=(const Vector<size, T>& other) {
            for(std::size_t i = 0; i != size; ++i)
                _data[i] -= other._data[i];

            return *this;
        }

        /**
         * @brief Subtract vector
         *
         * @see operator-=()
         */
        inline Vector<size, T> operator-(const Vector<size, T>& other) const {
            return Vector<size, T>(*this) -= other;
        }

        /**
         * @brief Multiply vector with number and assign
         *
         * The computation is done in-place. @f[
         *      \boldsymbol a_i = b \boldsymbol a_i
         * @f]
         */
        #ifdef DOXYGEN_GENERATING_OUTPUT
        template<class U> Vector<size, T>& operator*=(U number) {
        #else
        template<class U> inline typename std::enable_if<std::is_arithmetic<U>::value, Vector<size, T>&>::type operator*=(U number) {
        #endif
            for(std::size_t i = 0; i != size; ++i)
                _data[i] *= number;

            return *this;
        }

        /**
         * @brief Multiply vector with number
         *
         * @see operator*=(U), operator*(U, const Vector<size, T>&)
         */
        #ifdef DOXYGEN_GENERATING_OUTPUT
        template<class U> inline Vector<size, T> operator*(U number) const {
        #else
        template<class U> inline typename std::enable_if<std::is_arithmetic<U>::value, Vector<size, T>>::type operator*(U number) const {
        #endif
            return Vector<size, T>(*this) *= number;
        }

        /**
         * @brief Divide vector with number and assign
         *
         * The computation is done in-place. @f[
         *      \boldsymbol a_i = \frac{\boldsymbol a_i} b
         * @f]
         */
        #ifdef DOXYGEN_GENERATING_OUTPUT
        template<class U> Vector<size, T>& operator/=(U number) {
        #else
        template<class U> inline typename std::enable_if<std::is_arithmetic<U>::value, Vector<size, T>&>::type operator/=(U number) {
        #endif
            for(std::size_t i = 0; i != size; ++i)
                _data[i] /= number;

            return *this;
        }

        /**
         * @brief Divide vector with number
         *
         * @see operator/=(), operator/(U, const Vector<size, T>&)
         */
        #ifdef DOXYGEN_GENERATING_OUTPUT
        template<class U> inline Vector<size, T> operator/(U number) const {
        #else
        template<class U> inline typename std::enable_if<std::is_arithmetic<U>::value, Vector<size, T>>::type operator/(U number) const {
        #endif
            return Vector<size, T>(*this) /= number;
        }

        /**
         * @brief Multiply vector component-wise and assign
         *
         * The computation is done in-place. @f[
         *      \boldsymbol a_i = \boldsymbol a_i \boldsymbol b_i
         * @f]
         */
        template<class U> Vector<size, T>& operator*=(const Vector<size, U>& other) {
            for(std::size_t i = 0; i != size; ++i)
                _data[i] *= other._data[i];

            return *this;
        }

        /**
         * @brief Multiply vector component-wise
         *
         * @see operator*=(const Vector<size, U>&)
         */
        template<class U> inline Vector<size, T> operator*(const Vector<size, U>& other) const {
            return Vector<size, T>(*this) *= other;
        }

        /**
         * @brief Divide vector component-wise and assign
         *
         * The computation is done in-place. @f[
         *      \boldsymbol a_i = \frac{\boldsymbol a_i}{\boldsymbol b_i}
         * @f]
         */
        template<class U> Vector<size, T>& operator/=(const Vector<size, U>& other) {
            for(std::size_t i = 0; i != size; ++i)
                _data[i] /= other._data[i];

            return *this;
        }

        /**
         * @brief Divide vector component-wise
         *
         * @see operator/=(const Vector<size, U>&)
         */
        template<class U> inline Vector<size, T> operator/(const Vector<size, U>& other) const {
            return Vector<size, T>(*this) /= other;
        }

        /**
         * @brief Dot product of the vector
         *
         * Should be used instead of length() for comparing vector length with
         * other values, because it doesn't compute the square root. @f[
         *      \boldsymbol a \cdot \boldsymbol a = \sum_{i=0}^{n-1} \boldsymbol a_i^2
         * @f]
         * @see dot(const Vector&, const Vector&), isNormalized()
         */
        inline T dot() const {
            return dot(*this, *this);
        }

        /**
         * @brief %Vector length
         *
         * See also dot() const which is faster for comparing length with other
         * values. @f[
         *      |\boldsymbol a| = \sqrt{\boldsymbol a \cdot \boldsymbol a}
         * @f]
         * @see isNormalized()
         * @todo something like std::hypot() for possibly better precision?
         */
        inline T length() const {
            return std::sqrt(dot());
        }

        /**
         * @brief Normalized vector (of unit length)
         *
         * @see isNormalized()
         */
        inline Vector<size, T> normalized() const {
            return *this/length();
        }

        /**
         * @brief %Vector projected onto line
         *
         * Returns vector projected onto @p line. @f[
         *      \boldsymbol a_1 = \frac{\boldsymbol a \cdot \boldsymbol b}{\boldsymbol b \cdot \boldsymbol b} \boldsymbol b
         * @f]
         * @see projectedOntoNormalized()
         */
        inline Vector<size, T> projected(const Vector<size, T>& line) const {
            return line*dot(*this, line)/line.dot();
        }

        /**
         * @brief %Vector projected onto normalized line
         *
         * Slightly faster alternative to projected(), expects @p line to be
         * normalized. @f[
         *      \boldsymbol a_1 = \frac{\boldsymbol a \cdot \boldsymbol b}{\boldsymbol b \cdot \boldsymbol b} \boldsymbol b =
         *          (\boldsymbol a \cdot \boldsymbol b) \boldsymbol b
         * @f]
         */
        inline Vector<size, T> projectedOntoNormalized(const Vector<size, T>& line) const {
            CORRADE_ASSERT(line.isNormalized(), "Math::Vector::projectedOntoNormalized(): line must be normalized", (Vector<size, T>(std::numeric_limits<T>::quiet_NaN())));
            return line*dot(*this, line);
        }

        /** @brief Sum of values in the vector */
        T sum() const {
            T out(_data[0]);

            for(std::size_t i = 1; i != size; ++i)
                out += _data[i];

            return out;
        }

        /** @brief Product of values in the vector */
        T product() const {
            T out(_data[0]);

            for(std::size_t i = 1; i != size; ++i)
                out *= _data[i];

            return out;
        }

        /** @brief Minimal value in the vector */
        T min() const {
            T out(_data[0]);

            for(std::size_t i = 1; i != size; ++i)
                out = std::min(out, _data[i]);

            return out;
        }

        /** @brief Minimal absolute value in the vector */
        T minAbs() const {
            T out(std::abs(_data[0]));

            for(std::size_t i = 1; i != size; ++i)
                out = std::min(out, std::abs(_data[i]));

            return out;
        }

        /** @brief Maximal value in the vector */
        T max() const {
            T out(_data[0]);

            for(std::size_t i = 1; i != size; ++i)
                out = std::max(out, _data[i]);

            return out;
        }

        /** @brief Maximal absolute value in the vector */
        T maxAbs() const {
            T out(std::abs(_data[0]));

            for(std::size_t i = 1; i != size; ++i)
                out = std::max(out, std::abs(_data[i]));

            return out;
        }

    private:
        /* Implementation for Vector<size, T>::Vector(const Vector<size, U>&) */
        template<class U, std::size_t ...sequence> inline constexpr explicit Vector(Implementation::Sequence<sequence...>, const Vector<sizeof...(sequence), U>& vector): _data{T(vector._data[sequence])...} {}

        /* Implementation for Vector<size, T>::Vector(U) */
        template<std::size_t ...sequence> inline constexpr explicit Vector(Implementation::Sequence<sequence...>, T value): _data{Implementation::repeat(value, sequence)...} {}

        T _data[size];
};

/** @relates Vector
@brief Multiply number with vector

Same as Vector::operator*(U) const.
*/
#ifdef DOXYGEN_GENERATING_OUTPUT
template<std::size_t size, class T, class U> inline Vector<size, T> operator*(U number, const Vector<size, T>& vector) {
#else
template<std::size_t size, class T, class U> inline typename std::enable_if<std::is_arithmetic<U>::value, Vector<size, T>>::type operator*(U number, const Vector<size, T>& vector) {
#endif
    return vector*number;
}

/** @relates Vector
@brief Divide vector with number and invert

@f[
    \boldsymbol c_i = \frac b {\boldsymbol a_i}
@f]
@see Vector::operator/()
*/
#ifdef DOXYGEN_GENERATING_OUTPUT
template<std::size_t size, class T, class U> inline Vector<size, T> operator/(U number, const Vector<size, T>& vector) {
#else
template<std::size_t size, class T, class U> inline typename std::enable_if<std::is_arithmetic<U>::value, Vector<size, T>>::type operator/(U number, const Vector<size, T>& vector) {
#endif
    Vector<size, T> out;

    for(std::size_t i = 0; i != size; ++i)
        out[i] = number/vector[i];

    return out;
}

/** @debugoperator{Magnum::Math::Vector} */
template<std::size_t size, class T> Corrade::Utility::Debug operator<<(Corrade::Utility::Debug debug, const Vector<size, T>& value) {
    debug << "Vector(";
    debug.setFlag(Corrade::Utility::Debug::SpaceAfterEachValue, false);
    for(std::size_t i = 0; i != size; ++i) {
        if(i != 0) debug << ", ";
        debug << value[i];
    }
    debug << ")";
    debug.setFlag(Corrade::Utility::Debug::SpaceAfterEachValue, true);
    return debug;
}

/* Explicit instantiation for types used in OpenGL */
#ifndef DOXYGEN_GENERATING_OUTPUT
extern template Corrade::Utility::Debug MAGNUM_EXPORT operator<<(Corrade::Utility::Debug, const Vector<2, Float>&);
extern template Corrade::Utility::Debug MAGNUM_EXPORT operator<<(Corrade::Utility::Debug, const Vector<3, Float>&);
extern template Corrade::Utility::Debug MAGNUM_EXPORT operator<<(Corrade::Utility::Debug, const Vector<4, Float>&);
extern template Corrade::Utility::Debug MAGNUM_EXPORT operator<<(Corrade::Utility::Debug, const Vector<2, Int>&);
extern template Corrade::Utility::Debug MAGNUM_EXPORT operator<<(Corrade::Utility::Debug, const Vector<3, Int>&);
extern template Corrade::Utility::Debug MAGNUM_EXPORT operator<<(Corrade::Utility::Debug, const Vector<4, Int>&);
extern template Corrade::Utility::Debug MAGNUM_EXPORT operator<<(Corrade::Utility::Debug, const Vector<2, UnsignedInt>&);
extern template Corrade::Utility::Debug MAGNUM_EXPORT operator<<(Corrade::Utility::Debug, const Vector<3, UnsignedInt>&);
extern template Corrade::Utility::Debug MAGNUM_EXPORT operator<<(Corrade::Utility::Debug, const Vector<4, UnsignedInt>&);
#ifndef MAGNUM_TARGET_GLES
extern template Corrade::Utility::Debug MAGNUM_EXPORT operator<<(Corrade::Utility::Debug, const Vector<2, Double>&);
extern template Corrade::Utility::Debug MAGNUM_EXPORT operator<<(Corrade::Utility::Debug, const Vector<3, Double>&);
extern template Corrade::Utility::Debug MAGNUM_EXPORT operator<<(Corrade::Utility::Debug, const Vector<4, Double>&);
#endif
#endif

#ifndef DOXYGEN_GENERATING_OUTPUT
#define MAGNUM_VECTOR_SUBCLASS_IMPLEMENTATION(Type, size)                   \
    inline constexpr static Type<T>& from(T* data) {                        \
        return *reinterpret_cast<Type<T>*>(data);                           \
    }                                                                       \
    inline constexpr static const Type<T>& from(const T* data) {            \
        return *reinterpret_cast<const Type<T>*>(data);                     \
    }                                                                       \
                                                                            \
    inline Type<T>& operator=(const Type<T>& other) {                       \
        Math::Vector<size, T>::operator=(other);                            \
        return *this;                                                       \
    }                                                                       \
                                                                            \
    inline Type<T> operator-() const {                                      \
        return Math::Vector<size, T>::operator-();                          \
    }                                                                       \
    inline Type<T>& operator+=(const Math::Vector<size, T>& other) {        \
        Math::Vector<size, T>::operator+=(other);                           \
        return *this;                                                       \
    }                                                                       \
    inline Type<T> operator+(const Math::Vector<size, T>& other) const {    \
        return Math::Vector<size, T>::operator+(other);                     \
    }                                                                       \
    inline Type<T>& operator-=(const Math::Vector<size, T>& other) {        \
        Math::Vector<size, T>::operator-=(other);                           \
        return *this;                                                       \
    }                                                                       \
    inline Type<T> operator-(const Math::Vector<size, T>& other) const {    \
        return Math::Vector<size, T>::operator-(other);                     \
    }                                                                       \
    template<class U> inline typename std::enable_if<std::is_arithmetic<U>::value, Type<T>&>::type operator*=(U number) { \
        Math::Vector<size, T>::operator*=(number);                          \
        return *this;                                                       \
    }                                                                       \
    template<class U> inline typename std::enable_if<std::is_arithmetic<U>::value, Type<T>>::type operator*(U number) const { \
        return Math::Vector<size, T>::operator*(number);                    \
    }                                                                       \
    template<class U> inline typename std::enable_if<std::is_arithmetic<U>::value, Type<T>&>::type operator/=(U number) { \
        Math::Vector<size, T>::operator/=(number);                          \
        return *this;                                                       \
    }                                                                       \
    template<class U> inline typename std::enable_if<std::is_arithmetic<U>::value, Type<T>>::type operator/(U number) const { \
        return Math::Vector<size, T>::operator/(number);                    \
    }                                                                       \
    template<class U> inline Type<T>& operator*=(const Math::Vector<size, U>& other) { \
        Math::Vector<size, T>::operator*=(other);                           \
        return *this;                                                       \
    }                                                                       \
    template<class U> inline Type<T> operator*(const Math::Vector<size, U>& other) const { \
        return Math::Vector<size, T>::operator*(other);                     \
    }                                                                       \
    template<class U> inline Type<T>& operator/=(const Math::Vector<size, U>& other) { \
        Math::Vector<size, T>::operator/=(other);                           \
        return *this;                                                       \
    }                                                                       \
    template<class U> inline Type<T> operator/(const Math::Vector<size, U>& other) const { \
        return Math::Vector<size, T>::operator/(other);                     \
    }                                                                       \
                                                                            \
    inline Type<T> normalized() const { return Math::Vector<size, T>::normalized(); } \
    inline Type<T> projected(const Math::Vector<size, T>& other) const {    \
        return Math::Vector<size, T>::projected(other);                     \
    }

#define MAGNUM_VECTOR_SUBCLASS_OPERATOR_IMPLEMENTATION(Type, size)          \
    template<class T, class U> inline typename std::enable_if<std::is_arithmetic<U>::value, Type<T>>::type operator*(U number, const Type<T>& vector) { \
        return number*Math::Vector<size, T>(vector);                        \
    }                                                                       \
    template<class T, class U> inline typename std::enable_if<std::is_arithmetic<U>::value, Type<T>>::type operator/(U number, const Type<T>& vector) { \
        return number/Math::Vector<size, T>(vector);                        \
    }
#endif

}}

namespace Corrade { namespace Utility {

/** @configurationvalue{Magnum::Math::RectangularMatrix} */
template<std::size_t size, class T> struct ConfigurationValue<Magnum::Math::Vector<size, T>> {
    ConfigurationValue() = delete;

    /** @brief Writes elements separated with spaces */
    static std::string toString(const Magnum::Math::Vector<size, T>& value, ConfigurationValueFlags flags) {
        std::string output;

        for(std::size_t i = 0; i != size; ++i) {
            if(!output.empty()) output += ' ';
            output += ConfigurationValue<T>::toString(value[i], flags);
        }

        return output;
    }

    /** @brief Reads elements separated with whitespace */
    static Magnum::Math::Vector<size, T> fromString(const std::string& stringValue, ConfigurationValueFlags flags) {
        Magnum::Math::Vector<size, T> result;

        std::size_t oldpos = 0, pos = std::string::npos, i = 0;
        do {
            pos = stringValue.find(' ', oldpos);
            std::string part = stringValue.substr(oldpos, pos-oldpos);

            if(!part.empty()) {
                result[i] = ConfigurationValue<T>::fromString(part, flags);
                ++i;
            }

            oldpos = pos+1;
        } while(pos != std::string::npos);

        return result;
    }
};

#ifndef DOXYGEN_GENERATING_OUTPUT
/* Vectors */
extern template struct MAGNUM_EXPORT ConfigurationValue<Magnum::Math::Vector<2, Magnum::Float>>;
extern template struct MAGNUM_EXPORT ConfigurationValue<Magnum::Math::Vector<3, Magnum::Float>>;
extern template struct MAGNUM_EXPORT ConfigurationValue<Magnum::Math::Vector<4, Magnum::Float>>;
extern template struct MAGNUM_EXPORT ConfigurationValue<Magnum::Math::Vector<2, Magnum::Int>>;
extern template struct MAGNUM_EXPORT ConfigurationValue<Magnum::Math::Vector<3, Magnum::Int>>;
extern template struct MAGNUM_EXPORT ConfigurationValue<Magnum::Math::Vector<4, Magnum::Int>>;
extern template struct MAGNUM_EXPORT ConfigurationValue<Magnum::Math::Vector<2, Magnum::UnsignedInt>>;
extern template struct MAGNUM_EXPORT ConfigurationValue<Magnum::Math::Vector<3, Magnum::UnsignedInt>>;
extern template struct MAGNUM_EXPORT ConfigurationValue<Magnum::Math::Vector<4, Magnum::UnsignedInt>>;
#ifndef MAGNUM_TARGET_GLES
extern template struct MAGNUM_EXPORT ConfigurationValue<Magnum::Math::Vector<2, Magnum::Double>>;
extern template struct MAGNUM_EXPORT ConfigurationValue<Magnum::Math::Vector<3, Magnum::Double>>;
extern template struct MAGNUM_EXPORT ConfigurationValue<Magnum::Math::Vector<4, Magnum::Double>>;
#endif
#endif

}}

#endif