Consider the code snippet:

uint16_t ave_uint16_4x4_matrix(int xx, int yy, uint16_t **mat)  {
register uint32_t tot=0U, xi, yi;

// Sum 4 by 4 square
for(yi=yy; yi < yy+4; yi++)  {
    for(xi=xx; xi < xx+4; xi++)  {
        tot += mat[yi][xi];  
    }
}
tot >>= 4;  // BitShift to do quick Gozinta!  /= 16
return((uint16_t)tot);

}

The intent is to average a 4x4 chunk of a larger uint16_t matrix and produce a single result which should fit in a ushort (not tested).

With the AVX2 SIMD registers YMM0-YMM15, one value could be placed in each. With the 256 bit size, all 16 could be stacked in a single register.

The best AVX2 approach I can find would take at least 4 whacks at it. Is there a better way to add up all 16 uint16s and store the result in an int?

VPAVGW:: _mm256_avg_epu16 computes the average of 2 vectors.
Skylake 6700K, GCC Linux