奇怪的 cuBLAS gemm 批处理性能

Question

我注意到 cublasSgemmStriderdBatched 的一些奇怪表现，我正在寻找解释。矩阵大小固定为 20x20。以下是一些不同批次大小的一些时间安排（只有乘法，没有数据传输）：

• 批次 = 100，时间 = 0.2 毫秒
• 批次 = 1,000，时间 = 1.9 毫秒
• 批次 = 10,000，时间 = 18.3 毫秒
• 批次 = 100,000，时间 = 5.3 毫秒
• 批次 = 1,000,000，时间 = 52.8 毫秒

前几个批量大小与我预期的一样，随着批量大小增加十倍，时间线性增加。但是，使用 100,000 个矩阵突然会发生 3.4 倍的加速？

如果矩阵大小固定为 10x10 并再次执行试验，我发现：

• 批次 = 100，时间 = 0.2 毫秒
• 批次 = 1,000，时间 = 2.0 毫秒
• 批次 = 10,000，时间 = 20.0 毫秒
• 批次 = 100,000，时间 = 0.9 毫秒
• 批次 = 1,000,000，时间 = 8.9 毫秒

再一次，在 100,000 批大小下会出现惊人的 22 倍加速？让我想知道为什么 1,000 和 10,000 的批量大小比 100,000 的批量大小要慢，因为矩阵大小仍然是 10x10。

是否针对不同的批量大小使用了不同的算法？这种表现我觉得很奇怪。当我使用 cublasSgemmBatched 进行此试验时，会发生类似的结果。 这些试验在 GeForce GTX 1080 Ti 上执行。一个最小的工作代码被授予：

#include <stdio.h>
#include <stdlib.h>
#include "math.h"
#include "cublas_v2.h" 
//nvcc -lcublas cublas.c -o cublas.out

int main(int argc, char* argv[])
{
int i,j,k,index;

// Linear dimension of matrices
int dim = 20;
int batch_count = 10*10*10*10*10*1;
// Allocate host storage for batch_count A,B,C square matrices
float* h_A = malloc(sizeof(float) * dim * dim * batch_count);
float* h_B = malloc(sizeof(float) * dim * dim * batch_count);
float* h_C = malloc(sizeof(float) * dim * dim * batch_count);
    for(k=0; k<batch_count; k++) {
        for(j=0; j<dim; j++) {
                for(i=0; i<dim; i++) {
                index = i*dim + j + k*dim*dim;
                  h_A[index] = index*index + 0.0f;
                  h_B[index] = index + 1.0f;
                  h_C[index] = 0.0f;
        }
    }
}


float *d_A, *d_B, *d_C;
cudaMalloc(&d_A, sizeof(float) * dim * dim * batch_count);
cudaMalloc(&d_B, sizeof(float) * dim * dim * batch_count);
cudaMalloc(&d_C, sizeof(float) * dim * dim * batch_count);
cudaMemcpy(h_A,d_A,sizeof(float) * dim * dim * batch_count,cudaMemcpyDeviceToHost);
cudaMemcpy(h_B,d_B,sizeof(float) * dim * dim * batch_count,cudaMemcpyDeviceToHost);
cudaMemcpy(h_C,d_C,sizeof(float) * dim * dim * batch_count,cudaMemcpyDeviceToHost);

cublasHandle_t handle;
cublasCreate(&handle);

// Do the actual multiplication 
float time_cuda_event;
cudaEvent_t start, stop;    
cudaEventCreate(&start);
cudaEventCreate(&stop) ;
cudaEventRecord(start, 0);
float alpha = 1.0f;  float beta = 1.0f;
cublasSgemmStridedBatched(handle,
                              CUBLAS_OP_N, 
                              CUBLAS_OP_N,
                              dim, dim, dim,
                              &alpha,
                              (const float*)d_A, dim,
                              dim*dim,
                              (const float*)d_B, dim,
                              dim*dim,
                              &beta,
                              d_C, dim, 
                              dim*dim, 
                              batch_count);
( cudaEventRecord(stop, 0) );
( cudaEventSynchronize(stop) );
( cudaEventElapsedTime(&time_cuda_event, start, stop) );              
printf("Time :  %3.1f ms \n", time_cuda_event);  

cudaMemcpy(h_C,d_C,sizeof(float) * dim * dim * batch_count,cudaMemcpyDeviceToHost);
// Destroy the handle
cublasDestroy(handle);


cudaFree(d_A);
cudaFree(d_B);
cudaFree(d_C);
free(h_A);
free(h_B);
free(h_C);
    return 0;
}

Answer 1

这似乎只是 CUBLAS 中启发式的结果。如果我运行您的代码的修改（和工作）版本，我会得到 5x5 案例的这些时间：

Batch size :           10   Time :  0.019104 ms 
Batch size :          100   Time :  0.038304 ms 
Batch size :         1000   Time :  0.163520 ms 
Batch size :        10000   Time :  1.410944 ms 
Batch size :       100000   Time :  1.614144 ms 
Batch size :      1000000   Time :  16.057407 ms 

分析表明，在多达 10000 个条目的批次的情况下，库运行一个内核：

1.10759s  16.831us             (1 1 10)       (128 1 1)       120  12.250KB        0B         -           -           -           -  GeForce GTX 970         1         7  maxwell_sgemm_128x64_nn [3939]
1.10766s  19.168us            (1 1 100)       (128 1 1)       120  12.250KB        0B         -           -           -           -  GeForce GTX 970         1         7  maxwell_sgemm_128x64_nn [3971]
1.10773s  147.71us           (1 1 1000)       (128 1 1)       120  12.250KB        0B         -           -           -           -  GeForce GTX 970         1         7  maxwell_sgemm_128x64_nn [4003]
1.10791s  1.4064ms          (1 1 10000)       (128 1 1)       120  12.250KB        0B         -           -           -           -  GeForce GTX 970         1         7  maxwell_sgemm_128x64_nn [4035]

在更大的尺寸下，它会多次调用另一个内核来为调用提供服务：

1.10935s  1.1518ms          (1 1 65535)       (16 16 1)        31  2.1250KB        0B         -           -           -           -  GeForce GTX 970         1         7  void batch_gemm_kernel1x1_core<float, float, float, bool=0, bool=0, bool=0, bool=0, bool=0, bool=1, bool=1>(float* const *, float const * const *, float const * const *, float*, float const *, float const *, int, int, int, int, int, int, __int64, __int64, __int64, float const *, float const *, float, float, int, int) [4063]
1.11050s  606.54us          (1 1 34465)       (16 16 1)        31  2.1250KB        0B         -           -           -           -  GeForce GTX 970         1         7  void batch_gemm_kernel1x1_core<float, float, float, bool=0, bool=0, bool=0, bool=0, bool=0, bool=1, bool=1>(float* const *, float const * const *, float const * const *, float*, float const *, float const *, int, int, int, int, int, int, __int64, __int64, __int64, float const *, float const *, float, float, int, int) [4087]
1.11113s  1.1498ms          (1 1 65535)       (16 16 1)        31  2.1250KB        0B         -           -           -           -  GeForce GTX 970         1         7  void batch_gemm_kernel1x1_core<float, float, float, bool=0, bool=0, bool=0, bool=0, bool=0, bool=1, bool=1>(float* const *, float const * const *, float const * const *, float*, float const *, float const *, int, int, int, int, int, int, __int64, __int64, __int64, float const *, float const *, float, float, int, int) [4115]
1.11228s  1.1501ms          (1 1 65535)       (16 16 1)        31  2.1250KB        0B         -           -           -           -  GeForce GTX 970         1         7  void batch_gemm_kernel1x1_core<float, float, float, bool=0, bool=0, bool=0, bool=0, bool=0, bool=1, bool=1>(float* const *, float const * const *, float const * const *, float*, float const *, float const *, int, int, int, int, int, int, __int64, __int64, __int64, float const *, float const *, float, float, int, int) [4139]
1.11344s  1.1511ms          (1 1 65535)       (16 16 1)        31  2.1250KB        0B         -           -           -           -  GeForce GTX 970         1         7  void batch_gemm_kernel1x1_core<float, float, float, bool=0, bool=0, bool=0, bool=0, bool=0, bool=1, bool=1>(float* const *, float const * const *, float const * const *, float*, float const *, float const *, int, int, int, int, int, int, __int64, __int64, __int64, float const *, float const *, float, float, int, int) [4163]
1.11459s  1.1494ms          (1 1 65535)       (16 16 1)        31  2.1250KB        0B         -           -           -           -  GeForce GTX 970         1         7  void batch_gemm_kernel1x1_core<float, float, float, bool=0, bool=0, bool=0, bool=0, bool=0, bool=1, bool=1>(float* const *, float const * const *, float const * const *, float*, float const *, float const *, int, int, int, int, int, int, __int64, __int64, __int64, float const *, float const *, float, float, int, int) [4187]
1.11574s  1.1507ms          (1 1 65535)       (16 16 1)        31  2.1250KB        0B         -           -           -           -  GeForce GTX 970         1         7  void batch_gemm_kernel1x1_core<float, float, float, bool=0, bool=0, bool=0, bool=0, bool=0, bool=1, bool=1>(float* const *, float const * const *, float const * const *, float*, float const *, float const *, int, int, int, int, int, int, __int64, __int64, __int64, float const *, float const *, float, float, int, int) [4211]
1.11689s  1.1503ms          (1 1 65535)       (16 16 1)        31  2.1250KB        0B         -           -           -           -  GeForce GTX 970         1         7  void batch_gemm_kernel1x1_core<float, float, float, bool=0, bool=0, bool=0, bool=0, bool=0, bool=1, bool=1>(float* const *, float const * const *, float const * const *, float*, float const *, float const *, int, int, int, int, int, int, __int64, __int64, __int64, float const *, float const *, float, float, int, int) [4235]
1.11804s  1.1499ms          (1 1 65535)       (16 16 1)        31  2.1250KB        0B         -           -           -           -  GeForce GTX 970         1         7  void batch_gemm_kernel1x1_core<float, float, float, bool=0, bool=0, bool=0, bool=0, bool=0, bool=1, bool=1>(float* const *, float const * const *, float const * const *, float*, float const *, float const *, int, int, int, int, int, int, __int64, __int64, __int64, float const *, float const *, float, float, int, int) [4259]
1.11919s  1.1507ms          (1 1 65535)       (16 16 1)        31  2.1250KB        0B         -           -           -           -  GeForce GTX 970         1         7  void batch_gemm_kernel1x1_core<float, float, float, bool=0, bool=0, bool=0, bool=0, bool=0, bool=1, bool=1>(float* const *, float const * const *, float const * const *, float*, float const *, float const *, int, int, int, int, int, int, __int64, __int64, __int64, float const *, float const *, float, float, int, int) [4283]
1.12035s  1.1507ms          (1 1 65535)       (16 16 1)        31  2.1250KB        0B         -           -           -           -  GeForce GTX 970         1         7  void batch_gemm_kernel1x1_core<float, float, float, bool=0, bool=0, bool=0, bool=0, bool=0, bool=1, bool=1>(float* const *, float const * const *, float const * const *, float*, float const *, float const *, int, int, int, int, int, int, __int64, __int64, __int64, float const *, float const *, float, float, int, int) [4307]
1.12150s  1.1509ms          (1 1 65535)       (16 16 1)        31  2.1250KB        0B         -           -           -           -  GeForce GTX 970         1         7  void batch_gemm_kernel1x1_core<float, float, float, bool=0, bool=0, bool=0, bool=0, bool=0, bool=1, bool=1>(float* const *, float const * const *, float const * const *, float*, float const *, float const *, int, int, int, int, int, int, __int64, __int64, __int64, float const *, float const *, float, float, int, int) [4331]
1.12265s  1.1489ms          (1 1 65535)       (16 16 1)        31  2.1250KB        0B         -           -           -           -  GeForce GTX 970         1         7  void batch_gemm_kernel1x1_core<float, float, float, bool=0, bool=0, bool=0, bool=0, bool=0, bool=1, bool=1>(float* const *, float const * const *, float const * const *, float*, float const *, float const *, int, int, int, int, int, int, __int64, __int64, __int64, float const *, float const *, float, float, int, int) [4355]
1.12380s  1.1496ms          (1 1 65535)       (16 16 1)        31  2.1250KB        0B         -           -           -           -  GeForce GTX 970         1         7  void batch_gemm_kernel1x1_core<float, float, float, bool=0, bool=0, bool=0, bool=0, bool=0, bool=1, bool=1>(float* const *, float const * const *, float const * const *, float*, float const *, float const *, int, int, int, int, int, int, __int64, __int64, __int64, float const *, float const *, float, float, int, int) [4379]
1.12495s  1.1500ms          (1 1 65535)       (16 16 1)        31  2.1250KB        0B         -           -           -           -  GeForce GTX 970         1         7  void batch_gemm_kernel1x1_core<float, float, float, bool=0, bool=0, bool=0, bool=0, bool=0, bool=1, bool=1>(float* const *, float const * const *, float const * const *, float*, float const *, float const *, int, int, int, int, int, int, __int64, __int64, __int64, float const *, float const *, float, float, int, int) [4403]
1.12610s  1.1494ms          (1 1 65535)       (16 16 1)        31  2.1250KB        0B         -           -           -           -  GeForce GTX 970         1         7  void batch_gemm_kernel1x1_core<float, float, float, bool=0, bool=0, bool=0, bool=0, bool=0, bool=1, bool=1>(float* const *, float const * const *, float const * const *, float*, float const *, float const *, int, int, int, int, int, int, __int64, __int64, __int64, float const *, float const *, float, float, int, int) [4427]
1.12726s  1.1503ms          (1 1 65535)       (16 16 1)        31  2.1250KB        0B         -           -           -           -  GeForce GTX 970         1         7  void batch_gemm_kernel1x1_core<float, float, float, bool=0, bool=0, bool=0, bool=0, bool=0, bool=1, bool=1>(float* const *, float const * const *, float const * const *, float*, float const *, float const *, int, int, int, int, int, int, __int64, __int64, __int64, float const *, float const *, float, float, int, int) [4451]
1.12841s  299.35us          (1 1 16975)       (16 16 1)        31  2.1250KB        0B         -           -           -           -  GeForce GTX 970         1         7  void batch_gemm_kernel1x1_core<float, float, float, bool=0, bool=0, bool=0, bool=0, bool=0, bool=1, bool=1>(float* const *, float const * const *, float const * const *, float*, float const *, float const *, int, int, int, int, int, int, __int64, __int64, __int64, float const *, float const *, float, float, int, int) [4475]

您观察到的不一致似乎是由库中从一个内核到另一个内核的更改引起的，这可能是由某些批量大小标准造成的。您可以看到两个内核似乎每个批次项目使用一个块，较大尺寸的内核使用具有 256 个线程的 2D 块，而较小尺寸的内核使用具有 128 个线程的 1D 块。除此之外，性能差异取决于内部实现细节。尽管这样做可能违反了最终用户许可，但如果您想了解更多信息，您需要反汇编内核并查看它们的工作原理。该工具包包含执行此操作所需的所有工具，但我不建议您这样做。