I’m writing a GEMM code in C++, but the loop order actually influences a lot to the efficiency. Code:

// The first edition
void gemm_cpu_naive(
    int* __restrict__ C, 
    const int* __restrict__ A, 
    const int* __restrict__ B, 
    const int n, 
    const int m, 
    const int k){
    for(int l=0; l<k; ++l)
        for(int i=0; i<n; ++i)
            for(int j=0; j<m; ++j){
                C[i*m+j] += A[i*k+l] * B[l*m+j];
            }
}
// The second edition
void gemm_cpu_naive(
    int* __restrict__ C, 
    const int* __restrict__ A, 
    const int* __restrict__ B, 
    const int n, 
    const int m, 
    const int k){
    for(int i=0; i<n; ++i)
        for(int j=0; j<m; ++j)
            for(int l=0; l<k; ++l){
                C[i*m+j] += A[i*k+l] * B[l*m+j];
            }
}

n = 64, m = 64, k =64, the first edition cost 118 us, the second edition just cost 63 us.
The memory access pattern seems the same, A in row-order, B in column-order.
I searched a lot, one answer is the forst edition frequent writes to the same memory location, which can cause cache thrashing.

I wonder it’s the main cause of the huge difference of the efficiency? Or is the fact still undiscovered?