Why does this kernel not achieve peak IPC on a GK210? - cuda

Question

I decided that it would be educational for me to try to write a CUDA kernel that achieves peak IPC, so I came up with this kernel (host code omitted for brevity but is available here)
#define WORK_PER_THREAD 4
__global__ void saxpy_parallel(int n, float a, float *x, float *y)
{
int i = blockIdx.x*blockDim.x + threadIdx.x;
i *= WORK_PER_THREAD;
if (i < n)
{
#pragma unroll
for(int j=0; j<WORK_PER_THREAD; j++)
y[i+j] = a * x[i+j] + y[i+j];
}
}
I ran this kernel on a GK210, with n=32*1000000 elements, and expected to see an IPC of close to 4, but ended up with a lousy IPC of 0.186
ubuntu#ip-172-31-60-181:~/ipc_example$ nvcc saxpy.cu
ubuntu#ip-172-31-60-181:~/ipc_example$ sudo nvprof --metrics achieved_occupancy --metrics ipc ./a.out
==5828== NVPROF is profiling process 5828, command: ./a.out
==5828== Warning: Auto boost enabled on device 0. Profiling results may be inconsistent.
==5828== Profiling application: ./a.out
==5828== Profiling result:
==5828== Metric result:
Invocations Metric Name Metric Description Min Max Avg
Device "Tesla K80 (0)"
Kernel: saxpy_parallel(int, float, float*, float*)
1 achieved_occupancy Achieved Occupancy 0.879410 0.879410 0.879410
1 ipc Executed IPC 0.186352 0.186352 0.186352
I was even more confused when I set WORK_PER_THREAD=16, resulting in less threads launched, but 16, as opposed to 4, independent instructions for each to execute, the IPC dropped to 0.01
My two questions are:
What is the peak IPC I can expect on a GK210? I think it is 8 = 4 warp schedulers * 2 instruction dispatches per cycle, but I want to be sure.
Why does this kernel achieve such low IPC while achieved occupancy is high, why does IPC decrease as WORK_PER_THREAD increases, and how can I improve the IPC of this kernel?

Answer 1

What is the peak IPC I can expect on a GK210?
The peak IPC per SM is equal to the number of warp schedulers in an SM times the issue rate of each warp scheduler. This information can be found in the whitepaper for a particular GPU. The GK210 whitepaper is here. From that document (e.g. SM diagram on p8) we see that each SM has 4 warp schedulers capable of dual issue. Therefore the peak theoretically achievable IPC is 8 instructions per clock per SM. (however as a practical matter even for well-crafted codes, you're unlikely to see higher than 6 or 7).
Why does this kernel achieve such low IPC while achieved occupancy is high, why does IPC decrease as WORK_PER_THREAD increases, and how can I improve the IPC of this kernel?
Your kernel requires global transactions at nearly every operation. Global loads and even L2 cache loads have latency. When everything you do is dependent on those, there is no way to avoid the latency, so your warps are frequently stalled. The peak observable IPC per SM on a GK210 is somewhere in the vicinity of 6, but you won't get that with continuous load and store operations. Your kernel does 2 loads, and one store (12 bytes total moved), for each multiply/add. You won't be able to improve it. (Your kernel has high occupancy because the SMs are loaded up with warps, but low IPC because those warps are frequently stalled, unable to issue an instruction, waiting for latency of load operations to expire.) You'll need to find other useful work to do.
What might that be? Well if you do a matrix multiply operation, which has considerable data reuse and a relatively low number of bytes per math op, you're likely to see better measurements.
What about your code? Sometimes the work you need to do is like this. We'd call that a memory-bound code. For a kernel like this, the figure of merit to use for judging "goodness" is not IPC but achieved bandwidth. If your kernel requires a particular number of bytes loaded and stored to perform its work, then if we compare the kernel duration to just the memory transactions, we can get a measure of goodness. Stated another way, for a pure memory bound code (i.e. your kernel) we would judge goodness by measuring the total number of bytes loaded and stored (profiler has metrics for this, or for a simple code you can compute it directly by inspection), and divide that by the kernel duration. This gives the achieved bandwidth. Then, we compare that to the achievable bandwidth based on a proxy measurement. A possible proxy measurement tool for this is bandwidthTest CUDA sample code.
As the ratio of these two bandwidths approaches 1.0, your kernel is doing "well", given the memory bound work it is trying to do.