A simple header only vector math library for C++

vec3.hpp

#pragma once

#include <cmath>

namespace q {

    template <typename T>
    struct vec3 {
        union {
            struct { T x, y, z; };
            struct { T r, g, b; };
        };

        vec3() = default;
        vec3(T s): x(s), y(s), z(s) {}
        vec3(T _x, T _y, T _z) : x(_x), y(_y), z(_z) {}

        void normalize()
        {
            T m = length(*this);
            (*this).x /= m;
            (*this).y /= m;
            (*this).z /= m;
        }
    };

    template <typename T>
    vec3<T> operator*(const vec3<T>& a, const vec3<T>& b)
    { return vec3<T>(a.x * b.x, a.y * b.y, a.z * b.z); }

    template <typename T>
    vec3<T> operator/(const vec3<T>& a, const vec3<T>& b)
    { return vec3<T>(a.x / b.x, a.y / b.y, a.z / b.z); }

    template <typename T>
    vec3<T> operator+(const vec3<T> a, const vec3<T>& b)
    { return vec3<T>(a.x + b.x, a.y + b.y, a.z + b.z); }

    template <typename T>
    vec3<T> operator-(const vec3<T> a, const vec3<T>& b)
    { return vec3<T>(a.x - b.x, a.y - b.y, a.z - b.z); }

    template <typename T>
    T dot(const vec3<T>& a, const vec3<T>& b)
    { return a.x * b.x + a.y * b.y + a.z * b.z; }

    template <typename T>
    T length(const vec3<T>& a)
    { return std::sqrt(dot(a, a)); }

    template <typename T>
    vec3<T> cross(const vec3<T>& a, const vec3<T>& b)
    { return vec3<T>( a.y * b.z - a.z * b.y, \
                      a.z * b.x - a.x * b.z, \
                      a.x * b.y - a.y * b.x  ); }

    template <typename T>
    std::ostream& operator<<(std::ostream& o, const vec3<T>& v)
    { return o << "{ " << v.x << ", " << v.y << ", " << v.z << " }"; }

    typedef vec3<int>       vec3i;
    typedef vec3<float>     vec3f;
    typedef vec3<double>    vec3d;
};