Efficient method to check for matrix stability in

问题:

A number of algorithms iterate until a certain convergence criterion is reached (e.g. stability of a particular matrix). In many cases, one CUDA kernel must be launched per iteration. My question is: how then does one efficiently and accurately determine whether a matrix has changed over the course of the last kernel call? Here are three possibilities which seem equally unsatisfying:

• Writing a global flag each time the matrix is modified inside the kernel. This works, but is highly inefficient and is not technically thread safe.
• Using atomic operations to do the same as above. Again, this seems inefficient since in the worst case scenario one global write per thread occurs.
• Using a reduction kernel to compute some parameter of the matrix (e.g. sum, mean, variance). This might be faster in some cases, but still seems like overkill. Also, it is possible to dream up cases where a matrix has changed but the sum/mean/variance haven't (e.g. two elements are swapped).

Is there any of the three options above, or an alternative, that is considered best practice and/or is generally more efficient?

回答1:

I'll also go back to the answer I would have posted in 2012 but for a browser crash.

The basic idea is that you can use warp voting instructions to perform a simple, cheap reduction and then use zero or one atomic operations per block to update a pinned, mapped flag that the host can read after each kernel launch. Using a mapped flag eliminates the need for an explicit device to host transfer after each kernel launch.

This requires one word of shared memory per warp in the kernel, which is a small overhead, and some templating tricks can allow for loop unrolling if you provide the number of warps per block as a template parameter.

A complete working examplate (with C++ host code, I don't have access to a working PyCUDA installation at the moment) looks like this:

#include <cstdlib>
#include <vector>
#include <algorithm>
#include <assert.h>

__device__ unsigned int process(int & val)
{
    return (++val < 10);
}

template<int nwarps>
__global__ void kernel(int *inout, unsigned int *kchanged)
{
    __shared__ int wchanged[nwarps];
    unsigned int laneid = threadIdx.x % warpSize;
    unsigned int warpid = threadIdx.x / warpSize;

    // Do calculations then check for change/convergence 
    // and set tchanged to be !=0 if required
    int idx = blockIdx.x * blockDim.x + threadIdx.x;
    unsigned int tchanged = process(inout[idx]);

    // Simple blockwise reduction using voting primitives
    // increments kchanged is any thread in the block 
    // returned tchanged != 0
    tchanged = __any(tchanged != 0);
    if (laneid == 0) {
        wchanged[warpid] = tchanged;
    }
    __syncthreads();

    if (threadIdx.x == 0) {
        int bchanged = 0;
#pragma unroll
        for(int i=0; i<nwarps; i++) {
            bchanged |= wchanged[i];
        }
        if (bchanged) {
            atomicAdd(kchanged, 1);
        }
    }
}

int main(void)
{
    const int N = 2048;
    const int min = 5, max = 15;
    std::vector<int> data(N);
    for(int i=0; i<N; i++) {
        data[i] = min + (std::rand() % (int)(max - min + 1));
    }

    int* _data;
    size_t datasz = sizeof(int) * (size_t)N;
    cudaMalloc<int>(&_data, datasz);
    cudaMemcpy(_data, &data[0], datasz, cudaMemcpyHostToDevice);

    unsigned int *kchanged, *_kchanged;
    cudaHostAlloc((void **)&kchanged, sizeof(unsigned int), cudaHostAllocMapped);
    cudaHostGetDevicePointer((void **)&_kchanged, kchanged, 0);

    const int nwarps = 4;
    dim3 blcksz(32*nwarps), grdsz(16);

    // Loop while the kernel signals it needs to run again
    do {
        *kchanged = 0;
        kernel<nwarps><<<grdsz, blcksz>>>(_data, _kchanged);
        cudaDeviceSynchronize(); 
    } while (*kchanged != 0); 

    cudaMemcpy(&data[0], _data, datasz, cudaMemcpyDeviceToHost);
    cudaDeviceReset();

    int minval = *std::min_element(data.begin(), data.end());
    assert(minval == 10);

    return 0;
}

Here, kchanged is the flag the kernel uses to signal it needs to run again to the host. The kernel runs until each entry in the input has been incremented to above a threshold value. At the end of each threads processing, it participates in a warp vote, after which one thread from each warp loads the vote result to shared memory. One thread reduces the warp result and then atomically updates the kchanged value. The host thread waits until the device is finished, and can then directly read the result from the mapped host variable.

You should be able to adapt this to whatever your application requires

回答2:

I'll go back to my original suggestion. I've updated the related question with an answer of my own, which I believe is correct.

create a flag in global memory:

__device__ int flag;

at each iteration,

1. initialize the flag to zero (in host code):

   int init_val = 0;
   cudaMemcpyToSymbol(flag, &init_val, sizeof(int));
   

2. In your kernel device code, modify the flag to 1 if a change is made to the matrix:

   __global void iter_kernel(float *matrix){
   
   ...
     if (new_val[i] != matrix[i]){
       matrix[i] = new_val[i];
       flag = 1;}
   ...
   }
   

3. after calling the kernel, at the end of the iteration (in host code), test for modification:

   int modified = 0;
   cudaMemcpyFromSymbol(&modified, flag, sizeof(int));
   if (modified){
     ...
     }
   

Even if multiple threads in separate blocks or even separate grids, are writing the flag value, as long as the only thing they do is write the same value (i.e. 1 in this case), there is no hazard. The write will not get "lost" and no spurious values will show up in the flag variable.

Testing float or double quantities for equality in this fashion is questionable, but that doesn't seem to be the point of your question. If you have a preferred method to declare "modification" use that instead (such as testing for equality within a tolerance, perhaps).

Some obvious enhancements to this method would be to create one (local) flag variable per thread, and have each thread update the global flag variable once per kernel, rather than on every modification. This would result in at most one global write per thread per kernel. Another approach would be to keep one flag variable per block in shared memory, and have all threads simply update that variable. At the completion of the block, one write is made to global memory (if necessary) to update the global flag. We don't need to resort to complicated reductions in this case, because there is only one boolean result for the entire kernel, and we can tolerate multiple threads writing to either a shared or global variable, as long as all threads are writing the same value.

I can't see any reason to use atomics, or how it would benefit anything.

A reduction kernel seems like overkill, at least compared to one of the optimized approaches (e.g. a shared flag per block). And it would have the drawbacks you mention, such as the fact that anything less than a CRC or similarly complicated computation might alias two different matrix results as "the same".