Efficient operator+

Question

I have to compute large sums of 3d vectors and a comparison of using a vector class with overloaded operator+ and operator* versus summing up of separate components shows a performance difference of about a factor of three. I know assume the difference must be due to construction of objects in the overloaded operators.

How can one avoid the construction and improve performance?

I'm espacially puzzled, because the following is afaik basically the standard way to do it and I would expect the compiler to optimize this. In real life, the sums are not going to be done within a loop but in quite large expressions (several tens of MBs in total pre executable) summing up different vectors, this is why operator+ is used below.

class Vector 
{
   double x,y,z;
   ...
   Vector&  
   Vector::operator+=(const Vector &v)
   {
       x += v.x;
       y += v.y;
       z += v.z;
       return *this;
   }

   Vector  
   Vector::operator+(const Vector &v)
   {
       return Vector(*this) += v; // bad: construction and copy(?)
   }

   ...
}

// comparison
double xx[N], yy[N], zz[N];
Vector vec[N];

// assume xx, yy, zz and vec are properly initialized
Vector sum(0,0,0);
for(int i = 0; i < N; ++i)
{
    sum = sum + vec[i];
}

// this is a factor 3 faster than the above loop
double sumxx = 0;
double sumyy = 0;
double sumzz = 0;
for(int i = 0; i < N; ++i)
{
    sumxx = sumxx + xx[i];
    sumyy = sumyy + yy[i];
    sumzz = sumzz + zz[i];
}

Any help is greatly appreciated.

EDIT: Thank you all for your great input, I have the performance now at the same level. @Dima's and especially @Xeo's answer did the trick. I wish I could mark more than one answer "accepted". I'll test some of the other suggestions too.

Answer 1

This article has a really good argumentation on how to optimize operators such as +, -, *, /.
Implement the operator+ as a free function like this in terms of operator+=:

Vector operator+(Vector lhs, Vector const& rhs){
    return lhs += rhs;
}

Notice on how the lhs Vector is a copy and not a reference. This allowes the compiler to make optimizations such as copy elision.
The general rule that article conveys: If you need a copy, do it in the parameters, so the compiler can optimize. The article doesn't use this example, but the operator= for the copy-and-swap idiom.