Vectorized Matrix Multiplication - 2024.1 English

AI Engine-ML Kernel and Graph Programming Guide (UG1603)

Document ID
UG1603
Release Date
2024-06-06
Version
2024.1 English
The following is an example of a matrix multiplication with a (64 * 64) x (64 * 64) matrix size, and int8 x int8 data type. The matrix multiplication shape is 4*16*8. The input data is reshaped for matrix multiplication.
const int SHIFT=10;
//For element mmul
const int M=4;
const int K=16;
const int N=8;

//Total matrix sizes
const int rowA=64;
const int colA=64;
const int colB=64;

//mmul numbers
const int num_rowA=rowA/M; 
const int num_colA=colA/K;
const int num_colB=colB/N;

void matrix_mul(input_buffer<int8> & __restrict matA, input_buffer<int8> & __restrict matB, output_buffer<int8> & __restrict matC){
  using MMUL = aie::mmul<M, K, N, int8, int8>;
  
  const int8* __restrict pA=(int8*)matA.data();
  const int8* __restrict pB=(int8*)matB.data();
  int8* __restrict pC=(int8*)matC.data();

  //For profiling only 
  unsigned cycle_num[2];
  aie::tile tile=aie::tile::current();
  cycle_num[0]=tile.cycles();//cycle counter of the AI Engine tile

  int8 * __restrict pC1 = pC;
  for (unsigned i = 0; i < num_rowA; i++) {//for output row number of element matrix 
    for (unsigned j = 0; j < num_colB; j++) {//for output col number of element matrix
      const int8 * __restrict pA1 = pA + ( i * num_colA + 0) * MMUL::size_A;
      const int8 * __restrict pB1 = pB + ( 0 * num_colB + j) * MMUL::size_B;

      aie::vector<int8, MMUL::size_A> A0 = aie::load_v<MMUL::size_A>(pA1); pA1 += MMUL::size_A;
      aie::vector<int8, MMUL::size_B> B0 = aie::load_v<MMUL::size_B>(pB1); pB1 += MMUL::size_B * num_colB;

      MMUL C00; 
      C00.mul(A0, B0);

      for (unsigned k = 0; k < num_colA-1; k++) chess_prepare_for_pipelining {
        A0 = aie::load_v<MMUL::size_A>(pA1); pA1 += MMUL::size_A;
        B0 = aie::load_v<MMUL::size_B>(pB1); pB1 += MMUL::size_B * num_colB;
        C00.mac(A0, B0);
      }

      aie::store_v(pC1, C00.template to_vector<int8>(SHIFT)); pC1 += MMUL::size_C;
    }
  }

  //For profiling only 
  cycle_num[1]=tile.cycles();//cycle counter of the AI Engine tile
  printf("start=%d,end=%d,total=%d\n",cycle_num[0],cycle_num[1],cycle_num[1]-cycle_num[0]);
}

The profiled result shows that the loop takes around 3777 cycles. In total, this is 64*64*64=262144 multiplications on int8*int8 data type, which is 262144/3777 ~=69 int8*int8 MAC operations per cycle.

Note that the above result uses default settings for the AI Engine compiler, which will automatically run optimization-like loop pipelining for the loops.