# Unity Most efficient way of designing a vector class in 3D

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Recently I started to use unity3d for my hobby game project and I really liked a Vector3 (and similar) classes (in C#). At the moment at work I am implementing a simple (but for large simulations) SPH solver. What I would like to achieve is a similar Vector3 class in C++ in the means of access to elements both by v.x, v.y, v.z and v[0], v[1], v[2]. In general to obtain this is very simple, but none of the solutions that came to my mind is free of flaws.

Solution 1: using references &x, &y, &z, problem: such class has three additional variables which occupy the memory. In the case of large simulation it is problematic:

template <class T>
class Vector3
{
public:
T &x,&y,&z;
T v[3];

Vector3(): x(v[0]), y(v[1]), z(v[2])
{
v[0]=0; v[1]=1;  v[2]=2;
}

T& operator[](int i)
{
return v[i];
}
};

The access is very elegant:

v[i]

as well as

v.x, v.y and v.z

And this is what I woluld like to obtain - this elegant access. However the additional memory overhead is unacceptable.

Solution 2: using class fileds x,y,z and access operator with if statement: problem performance of [] operator

template <class T>
class Vector3
{
public:
T x,y,z;

Vector3(): x(0), y(1), z(2)
{ }

T& operator[](int i)
{
if (i==0) return x;
else if (i==1) return y;
else if (i==2) reurn z;
else
{
//throw access error
}
}
};

This solution is elegant as well, but the operator [] will be very slow.

Solution 3: Using the class functions x(), y(), z()

template <class T>
class Vector3
{
public:
T v[3];

Vector3()
{
v[0]=0; v[1]=1; v[2]=2;
}

T& operator[](int i)
{
return v[i];
}

T& x() { return v[0]; }
T& y() { return v[1]; }
T& z() { return v[2]; }
};

This solution is ideal in means of efficiency and memory overhead, but, does not allow elegant access to members, requires for example v.x() instead of v.x.

The question is: is there a way to obtain this elegant access with no efficiency and memory loss?

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Yeah union with anonymous struct has got to be the easiest way to do it,

template <class T>
struct Vector3
{
union
{
T v[3];
struct { T x; T y; T z; };
};
};

Edited by Syntac_

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Couldn't you just use the array access? Will you later want to add r, g, b, a and s, t or u, v?

namespace vectors {

enum accessors {
x,
y,
z,
w
};

template <typename T>
struct Vector4
{
T d[4];
T& operator[](size_t index);
const T& operator[](size_t index) const;
};

}



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How does that code allow me to write "v.x"?

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Sorry I forgot to include the operator to be able access like v[0].

template <class T>
struct Vector3
{
union
{
T v[3];
struct { T x;  T y; T z; };
};

T& operator[](int i)
{
// guard against accessing out-of-bounds
return v[i];
}
};

Vector3<float> v;
v.x = 3.0f;

std::cout << v[0]; // prints 3


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How does that code allow me to write "v.x"?

It does not really need to and avoids weird workarounds/UB for a questionable convenience.

But you can easily do:

using namespace vectors;

float bar(const Vector4<float>& v) {
return v[x];
}


Edited by wintertime

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Re-iterating what Hodgman wrote, these arrays of floats are functional but not ideal.

If you are looking for performance most systems will use built-in SIMD structures for the data that are specific to the system you are developing for.  That can mean the intrinsic type __m128 variables in the x86 family, or the intrinsic float32x4_t variables in ARM chips.

Transferring to and from these packed, special-purpose registers is not efficient. If possible leave your data packed in the more efficient formats.

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Solution 4

union
{
float v[3];
struct { float x, float y, float z; };
}

Yeah union with anonymous struct has got to be the easiest way to do it,

Union-based type-punning is non-standard. It is supported by both GCC and Visual Studio, so I use it, but it's important to remember that it's not guaranteed by the standard.

I've heard talk of them standardizing it in a future C++ standard, but I'm not sure if they already did that (in C++14 maybe?), or if they are intending to do it, what the status is on it.

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My vector class is basically:

Vector<ComponentType, Dimensions>

With typedefs as:

Vec2f

Vec3i

Vec4ui

etc. (for all primitive types for dimensions 1-4)

And I chose to ONLY allow array subscript access:

myVector[0] = 1.0f;

For matrices (similar in all other aspects), I instead use call operator overload:

myMatrix(0,0) = 1.0f;

Because Im not going to make a fancy proxy class just so I can use [].

Its just 2 extra characters so I didnt see a reason to hack support for x,y,z,w. Those dont even allow indexing by variable (which is usually needed to avoid code repetition) so it would be a messy combination of array style access and letters, which would probably just lead to bugs and harder to understand code.

Ill have to add Vector.swizzle(indices) (as in glsls vec.xz for example) because lack of having that has annoyed me recently...

If I were to add x,y,z I would probably just use methods named x() y() z() for them. That way I could implement the swizzle stuff like xy() xz() and so on using same syntax.

EDIT:

Also I love how VS2015 can create the method definition body for me because creating those by hand is not fun with these template classes...

Edited by Waterlimon

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If you really need vector types like this then I would say just use GLM, but if you want performance then I would say stay away from class VectorN...

If you do want a simple vector type and you don't want to use GLM you could use the following in Clang anyway:

using Vector3 = float __attribute__((ext_vector_type(3)));
//Vector3 is pretty much identical to vec3 or float3 from GLSL or HLSL

Edited by Chris_F

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This is an article from one of the Insomniac Games developers that discusses SIMD instructions and the problem with using vector classes: https://deplinenoise.files.wordpress.com/2015/03/gdc2015_afredriksson_simd.pdf

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Solution 4

union
{
float v[3];
struct { float x, float y, float z; };
}

Yeah union with anonymous struct has got to be the easiest way to do it,

Union-based type-punning is non-standard. It is supported by both GCC and Visual Studio, so I use it, but it's important to remember that it's not guaranteed by the standard.

I've heard talk of them standardizing it in a future C++ standard, but I'm not sure if they already did that (in C++14 maybe?), or if they are intending to do it, what the status is on it.

Yeah it's not, but the world will collapse (literally) so this will never be changed.

Additional tip. It is currently better to implement the methods of the vector class using v[] instead of x,y,z, becase for some reason(at least msvc) the compiler doesn't know that x,y,z are sequental in memory, thus wont use the multiple lane SIMD instructions (for example movss could be used multiple times instead of one movups).

EDIT: I saf the fastcall22 answer; My mistake this was on VS2013, I really don't know about 2015

Edited by imoogiBG

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for some reason(at least msvc) the compiler doesn't know that x,y,z are sequental in memory, thus wont use the multiple lane SIMD instructions.

Hmm? I don't think this is true. Or am I misunderstanding? I recently SIMD-ified an inner loop in one of my projects and compared the assembly before and after. I was using a home-grown xywz vector4 and Visual Studio 2015 properly used the *PS instructions.

When I get home today, I can double check.

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Hmm? I don't think this is true. Or am I misunderstanding? I recently SIMD-ified an inner loop in one of my projects and compared the assembly before and after. I was using a home-grown xywz vector4 and Visual Studio 2015 properly used the *PS instructions.

Automatic vectorization sometimes works, sometimes doesn't.  If the compiler happens to recognize a specific pattern it might do it in parallel.

The problem is that the result isn't guaranteed.  It is an optimization that sometimes the compiler does, but it could easily stop doing due to a minor change in the code, or an update to the compiler and build tools.

And there are many cases where the code could be easily made SIMD where the compiler doesn't recognize it. The programmer could take some few simple actions and vectorize loops with little work.

If you want to actually rely on SIMD, you need to explicitly code for it.

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I see automatic vectorization as a way to get a free performance boost from old code by simply recompiling it. If you are writing new code with performance in mind you should not count on the compiler automatically doing anything for you.

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In MathGeoLib I use Hodgman's method, see https://github.com/juj/MathGeoLib/blob/master/src/Math/float3.h#L104 , and that has worked well in practice. For float4 type and __m128 support, I use the union approach, see https://github.com/juj/MathGeoLib/blob/master/src/Math/float4.h#L56 . I favor using those over fancy template accesses, simply because the generated intermediate code is much straightforward, and the code also looks cleaner. (and I extensively unit test on MinGW32/MingW64/GCC/Clang/MSVCs on different platforms so I know when the code is good or not for the platforms I care. Nothing beats rigorous automated testing when it comes to having a peace of mind for correctness)

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This has been solved by others previously. Here's a thread I had bookmarked about it, with a nice solution:

http://www.gamedev.net/topic/261920-a-slick-trick-in-c/

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I'm sorry that I have nothing to add, but I never knew that creating a vector class was so difficult! I've learned a great deal just be reading. I'll have to completely reconsider how I implement this in the future.

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