Counting Threads in a Launch

__global__ void scale(float* x, int n, float a) {
    int i = blockIdx.x * blockDim.x + threadIdx.x;
    if (i < n) x[i] = a * x[i];
}

int n       = 1000000;
int threads = 256;
int blocks  = (n + threads - 1) / threads;   // 3907
scale<<<blocks, threads>>>(d_x, n, 2.0f);

How many threads does this launch start, how many warps is that, and what do the leftover threads do?

3,907 threads, one per block, each looping over its own 256 elements.

1,000,192 threads, and the extra 192 write past the end of x, since the guard runs after the index has already been used.

3,907 blocks x 256 threads = 1,000,192 threads, which is 31,256 warps of 32; the last 192 threads fail the i < n guard and exit without touching memory.

Exactly 1,000,000 threads, because the guard stops the extra threads from being created.

1,000,192 threads in 3,907 warps, since a warp is the hardware name for a block.