Understand whether code sample is CPU bound or Memory bound

Question

As a general question to those working on optimization and performance tuning of programs, how do you figure out if your code is CPU bound or Memory bound? I understand these concepts in general, but if I have say, 'y' amounts of loads and stores and '2y' computations, how does one go about finding what is the bottleneck?

Also can you figure out where exactly you are spending most of your time and say, if you load 'x' amount of data into cache (if its memory bound), in every loop iteration, then your code will run faster? Is there any precise way to determine this 'x', other than trial and error?

Are there any tools that you'll use, say on the IA-32 or IA-64 architecture? Doest VTune help?

For example, I'm currently doing the following:

I have 26 8*8 matrices of complex doubles and I have to perform a MVM (matrix vector multiplication) with (~4000) vectors of length 8, for each of these 26 matrices. I use SSE to perform the complex multiplication.

/*Copy 26 matrices to temporary storage*/
for(int i=0;i<4000;i+=2){//Loop over the 4000 vectors 
    for(int k=0;k<26;k++){//Loop over the 26 matrices
       /*
        Perform MVM in blocks of '2' between kth matrix and 
        'i' and 'i+1' vector
       */     

    }
}

The 26 matrices take 26kb (L1 cache is 32KB) and I have laid the vectors out in memory such that I have stride'1' accesses. Once I perform MVM on a vector with the 27 matrices, I don't visit them again, so I don't think cache blocking will help. I have used vectorization but I'm still stuck on 60% of peak performance.

I tried copying, say 64 vectors, into temporary storage, for every iteration of the outer loop thinking they'll be in cache and help, but its only decreased performance. I tried using _mm_prefetch() in the following way: When I am done with about half the matrices, I load the next 'i' and 'i+1' vector into memory, but that too hasn't helped.

I have done all this assuming its memory bound but I want to know for sure. Is there a way?

Answer 1

To my understanding the best way is profiling your application/workload. Based on the input data, the characteristic of the application/workload can significantly vary. These behaviors can however be quantified with to few phases Ref[2, 3] and a histogram can broadly tell the most frequent path of the workload to be optimized. The question that you are asking will also require benchmark programs [like SPEC2006, PARSEC, Media bench etc] for an architecture and is difficult to answer in general terms ( and is an active part of research in computer architecture). However, for specific cases a quantitative result can be stated for different memory hierarchies. You can use tools like:

• Perf
• OProfile
• VTune
• LikWid
• LLTng

and other monitoring and simulation tools to get the profiling traces of the application. You can look at performance counters like IPC, CPI ( for CPU bound) and memory access, cache misses, cache access , and other memory counters for determining memory boundedness.like IPC, Memory access per cycle (MPC), is often used to determine the memory boundedness of an application/workload. To specifically improve matrix multiplication, I would suggest using a optimized algorithm as in LAPACK.