index in threadId in Cuda - cuda

Question

Here is a short code I get from "Introduction to parallel computation" in udacity. The index in this code confuse me.
__global__ void use_shared_memory_GPU(float *array)
{
int i, index = threadIdx.x;
float average, sum=0.0f;
__shared__ float sh_arr[128];
sh_arr[index] = array[index];
__syncthreads();
// Now it begins to confuse me
for(i=0; i<index; i++) { sum += sh_arr[i]; } // what is the index here?
average = sum / (index + 1.0f); // what is the index here?
// why add 1.0f?
if(array[index] > average) {array[index] = average;}
}
The index is created as the Id for each thread, which I can understand. But when calculate the average, the index is used as number of threads. The first index used as a parallel computation id for arrays, while the second index is used just as common c. I repeat this procedure in my program, but the result doesn't repeat.
What's the trick behind the index? I print it in cuda-gdb, it just shows 0. Any detailed explanation for this?
Add one point. When calculate the average, why it adds 1.0f?

Answer 1

This code is computing prefix sums. A prefix sum for an array of values looks like this:
array: 1 2 4 3 5 7
prefix-sums: 1 3 7 10 15 22
averages: 1 2 2.33 2.25 3 3.67
index: 0 1 2 3 4 5
Each prefix sum is the sum of elements in the value array up to that position.
The code is also computing the "average" which is the prefix sum divided by the number of elements used to compute the sum.
In the code you have shown, each thread is computing a different element of the prefix-sum array (and a separate average).
Therefore, to compute the given average in each thread, we take the prefix-sum and divide by the index, but we must add 1 to the index, since adding 1 to the index gives us the number of elements used to compute the prefix-sum (and average) for that thread.