SIMD prefix sum on Intel cpu

I need to implement a prefix sum algorithm and would need it to be as fast as possible.
Ex:

[3, 1,  7,  0,  4,  1,  6,  3]

should give:

[3, 4, 11, 11, 15, 16, 22, 25]

Is there a way to do this using SSE SIMD CPU instruction?

My first idea is to sum each pair in parallel recursively until all sum have been computed like below!

//in parallel do 
for (int i = 0; i < z.length; i++) {
    z[i] = x[i << 1] + x[(i << 1) + 1];
}

To make the algorithm a little bit more clear, z is not the final output, but instead used to compute the output.

int[] w = computePrefixSum(z);
for (int i = 1; i < ouput.length; i++) {
    ouput[i] = (i % 2 == 0) ? (x[i] + ouput[i - 1]) :  w[(i - 1) >> 1];
}