struct float3
{
    float x, y, z;
};

float3
operator +(float3 a, float3 b) {
    return {
        a.x + b.x,
        a.y + b.y,
        a.z + b.z,
    };
}

float3
operator -(float3 a, float3 b) {
    return {
        a.x - b.x,
        a.y - b.y,
        a.z - b.z,
    };
}

float3
operator *(float3 a, float scalar) {
    return {
        a.x * scalar,
        a.y * scalar,
        a.z * scalar,
    };
}


static float
LenSqr(float3 v)
{
    float sum = v.x * v.x + v.y * v.y + v.z * v.z;
    return sum;
}

static float
Len(float3 v)
{
    return sqrtf(LenSqr(v));
}

static float3
Norm(float3 v)
{
    float len = Len(v);
    v.x = v.x / len;
    v.y = v.y / len;
    v.z = v.z / len;
    return v;
}

static float
Dot(float3 a, float3 b)
{
    return a.x * b.x + a.y * b.y + a.z * b.z;
}

float3
Cross(float3 a, float3 b)
{
    return {
        a.y * b.z - a.z * b.y,
        a.z * b.x - a.x * b.z,
        a.x * b.y - a.y * b.x,
    };
}