The following is an example of
(64 * 64) x (64 *
64)
int8 x int8
matrix multiplication kernel code. 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_window<int8> * __restrict matA, input_window<int8> * __restrict matB, output_window<int8> * __restrict matC){
using MMUL = aie::mmul<M, K, N, int8, int8>;
const int8* __restrict pA=(int8*)matA->ptr;
const int8* __restrict pB=(int8*)matB->ptr;
int8* __restrict pC=(int8*)matC->ptr;
//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 5500 cycles. In total,
this is 64*64*64=262144 multiplications on int8*int8
data
type, which is 262144/5500 ~=48 int8*int8
MAC operations
per cycle.
Add
-v
to aiecompiler
, and look at the compilation
of kernel log in Work/aie/<COL_ROW>/<COL_ROW>.log
:
HW do-loop #765 in ".../matrix_mul.cc", line 43: (loop #13) :
critical cycle of length 4 : b97 -> b99 -> b101 -> b102 -> b103 -> b104 -> b97
minimum length due to resources: 4
scheduling HW do-loop #765
(algo 1a) -> # cycles: 13
(modulo) -> # cycles: 4i 5i 6 ok (required budget ratio: 1)
(resume algo) -> after folding: 6 (folded over 2 iterations)
-> HW do-loop #765 in ".../Vitis/2022.1/aietools/include/aie_api/detail/aie1/mmul_8_8.hpp", line 278: (loop #13) : 6 cycles
The resource limitation is 4, however it takes 6 cycles for each loop
iteration for the inner most loop. Besides, the inner loop only has loop count
num_colA-1=3
. So it is worthwhile to see if flattening the loop
and letting tool pipeline larger amount of instructions in outer loop helps. The adjusted
instructions for the loop is as
follows:for (unsigned i = 0; i < num_rowA; i++) {
for (unsigned j = 0; j < num_colB; j++) chess_prepare_for_pipelining {
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_flatten_loop {
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;
}
}
With above instruction adjustment, the achieved latency of the loop is around
3472 cycles, which is roughly 262144/3472 ~=61 int8*int8
MACs per cycle.