我正在尝试优化在单核上运行的矩阵乘法代码。我如何进一步改善循环展开FMA / SSE的性能?我也很好奇,如果在内部循环中使用四个而不是两个总和,为什么性能不会提高。
问题大小是1000x1000的矩阵乘法。 gcc 9和icc 19.0.5均可用。 Intel Xeon @ 3.10GHz,32K L1d缓存,Skylake架构。编译为gcc -O3 -mavx
。
void mmult(double* A, double* B, double* C)
{
const int block_size = 64 / sizeof(double);
__m256d sum[2], broadcast;
for (int i0 = 0; i0 < SIZE_M; i0 += block_size) {
for (int k0 = 0; k0 < SIZE_N; k0 += block_size) {
for (int j0 = 0; j0 < SIZE_K; j0 += block_size) {
int imax = i0 + block_size > SIZE_M ? SIZE_M : i0 + block_size;
int kmax = k0 + block_size > SIZE_N ? SIZE_N : k0 + block_size;
int jmax = j0 + block_size > SIZE_K ? SIZE_K : j0 + block_size;
for (int i1 = i0; i1 < imax; i1++) {
for (int k1 = k0; k1 < kmax; k1++) {
broadcast = _mm256_broadcast_sd(A+i1*SIZE_N+k1);
for (int j1 = j0; j1 < jmax; j1+=8) {
sum[0] = _mm256_load_pd(C+i1*SIZE_K+j1+0);
sum[0] = _mm256_add_pd(sum[0], _mm256_mul_pd(broadcast, _mm256_load_pd(B+k1*SIZE_K+j1+0)));
_mm256_store_pd(C+i1*SIZE_K+j1+0, sum[0]);
sum[1] = _mm256_load_pd(C+i1*SIZE_K+j1+4);
sum[1] = _mm256_add_pd(sum[1], _mm256_mul_pd(broadcast, _mm256_load_pd(B+k1*SIZE_K+j1+4)));
_mm256_store_pd(C+i1*SIZE_K+j1+4, sum[1]);
// doesn't improve performance.. why?
// sum[2] = _mm256_load_pd(C+i1*SIZE_K+j1+8);
// sum[2] = _mm256_add_pd(sum[2], _mm256_mul_pd(broadcast, _mm256_load_pd(B+k1*SIZE_K+j1+8)));
// _mm256_store_pd(C+i1*SIZE_K+j1+8, sum[2]);
// sum[3] = _mm256_load_pd(C+i1*SIZE_K+j1+12);
// sum[3] = _mm256_add_pd(sum[3], _mm256_mul_pd(broadcast, _mm256_load_pd(B+k1*SIZE_K+j1+12)));
// _mm256_store_pd(C+i1*SIZE_K+j1+4, sum[3]);
}
}
}
}
}
}
}
此代码每个FMA有2个负载(如果发生FMA收缩),但是理论上Skylake每个FMA仅支持至多