Vectorized Version Using Multiple Kernels

With one input data per cycle, as estimated in Design Analysis, you must run four kernels in parallel to get the best throughput. One such solution is to divide 32 coefficients into four kernels, where data is broadcast to four kernels. The partial accumulation results from kernels can be cascaded to produce result in the last kernel. The implementation is shown in the following figure:

Figure 1. Data Broadcast to 4 Kernels

Note that part of the initial data is discarded in subsequent kernels. For example, the second kernel will discard the first eight inputs.

Four lanes and eight points are chosen for aie::sliding_mul. Data reads and writes are interleaved with computation.

The first kernel code is as follows:

alignas(aie::vector_decl_align) static cint16 eq_coef0[8]={{1,2},{3,4},...};

//For storing data between graph iterations
static aie::vector<cint16,16> delay_line;
__attribute__((noinline)) void fir_32tap_core0(input_stream<cint16> * sig_in,
      output_stream<cacc48> * cascadeout){
  const cint16_t * restrict coeff = eq_coef0;
  const aie::vector<cint16,8> coe = aie::load_v<8>(coeff);

  aie::vector<cint16,16> buff = delay_line;
  aie::accum<cacc48,4> acc;
  const unsigned LSIZE = (SAMPLES/4/4); // assuming samples is integer power of 2 and greater than 16

  main_loop:for (unsigned int i = 0; i < LSIZE; ++i)
  chess_prepare_for_pipelining
  {
    //8 MAC produce 4 partial output
    buff.insert(2,readincr_v<4>(sig_in));
    acc = aie::sliding_mul<4,8>(coe,0,buff,0);
    writeincr(cascadeout,acc);

    //8 MAC produce 4 partial output
    buff.insert(3,readincr_v<4>(sig_in));
    acc = aie::sliding_mul<4,8>(coe,0,buff,4);
    writeincr(cascadeout,acc);

    buff.insert(0,readincr_v<4>(sig_in));
    acc = aie::sliding_mul<4,8>(coe,0,buff,8);
    writeincr(cascadeout,acc);

    buff.insert(1,readincr_v<4>(sig_in));
    acc = aie::sliding_mul<4,8>(coe,0,buff,12);
    writeincr(cascadeout,acc);
  }
  delay_line = buff;
}
void fir_32tap_core0_init(){
  // Drop samples if not first block
  int const Delay = 0;
  for (int i = 0; i < Delay; ++i){
    get_ss(0);
  }
  //initialize data
  for (int i=0;i<8;i++){
    int tmp=get_ss(0);
    delay_line.set(*(cint16*)&tmp,i);
  }
};

Note:

__attribute__((noinline)) is optional to keep function hierarchy.
chess_prepare_for_pipelining is optional as the tools can do automatic pipelining.
Each aie::sliding_mul<4,8> is multiplying four lanes eight points MAC and the partial result is sent through the cascade chain to the next kernel.
Data buff is read starting from data_start parameter of aie::sliding_mul. The kernel code goes back to the beginning when it reaches the end in a circular fashion.

The compilation report can be found in Work/aie/<COL_ROW>/<COL_ROW>.log and the -v option is needed to generate the verbose report. In the log, search keywords, such as do-loop, to find the initiation interval of the loop. In the following example log file, you can see that the initiating interval of the loop is 16:

(resume algo) -> after folding: 16 (folded over 1 iterations)
-> HW do-loop #128 in ".../Vitis/2023.2/aietools/include/adf/stream/me/stream_utils.h", line 1192: (loop #3) : 16 cycles

Tip: Get the last reported cycle for the loop in the log file.

The kernel code above takes roughly 16 (cycles) / 16 (partial results) = 1 cycle to produce a partial output.

The other three kernels are similar. The second kernel code is as follows:

alignas(aie::vector_decl_align) static cint16 eq_coef2[8]={{17,18},{19,20},...};

//For storing data between graph iterations
alignas(aie::vector_decl_align) static aie::vector<cint16,16> delay_line;

__attribute__((noinline)) void fir_32tap_core1(input_stream<cint16> * sig_in, input_stream<cacc48> * cascadein,
      output_stream<cacc48> * cascadeout){
  const aie::vector<cint16,8> coe = aie::load_v<8>(eq_coef1);
  aie::vector<cint16,16> buff = delay_line;
  aie::accum<cacc48,4> acc;
  const unsigned LSIZE = (SAMPLES/4/4); // assuming samples is integer power of 2 and greater than 16

  for (unsigned int i = 0; i < LSIZE; ++i)
  chess_prepare_for_pipelining
  {
    //8 MAC produce 4 partial output
    acc = readincr_v4(cascadein);
    buff.insert(2,readincr_v<4>(sig_in));
    acc = aie::sliding_mac<4,8>(acc,coe,0,buff,0);
    writeincr_v4(cascadeout,acc);

    acc = readincr_v4(cascadein);
    buff.insert(3,readincr_v<4>(sig_in));
    acc = aie::sliding_mac<4,8>(acc,coe,0,buff,4);
    writeincr_v4(cascadeout,acc);

    acc = readincr_v4(cascadein);
    buff.insert(0,readincr_v<4>(sig_in));
    acc = aie::sliding_mac<4,8>(acc,coe,0,buff,8);
    writeincr_v4(cascadeout,acc);

    acc = readincr_v4(cascadein);
    buff.insert(1,readincr_v<4>(sig_in));
    acc = aie::sliding_mac<4,8>(acc,coe,0,buff,12);
    writeincr_v4(cascadeout,acc);
  }
  delay_line = buff;
}
void fir_32tap_core1_init()
{
  // Drop samples if not first block
  int const Delay = 8;
  for (int i = 0; i < Delay; ++i){
    get_ss(0);
  }
  //initialize data
  for (int i=0;i<8;i++){
    int tmp=get_ss(0);
    delay_line.set(*(cint16*)&tmp,i);
  }
};

The third kernel code is as follows:

alignas(aie::vector_decl_align) static cint16 eq_coef2[8]={{33,34},{35,36},...};

//For storing data between graph iterations
alignas(aie::vector_decl_align) static aie::vector<cint16,16> delay_line;
__attribute__((noinline)) void fir_32tap_core2(input_stream<cint16> * sig_in, input_stream<cacc48> * cascadein,
      output_stream<cacc48> * cascadeout){
  const aie::vector<cint16,8> coe = aie::load_v<8>(eq_coef2);
  aie::vector<cint16,16> buff = delay_line;
  aie::accum<cacc48,4> acc;
  const unsigned LSIZE = (SAMPLES/4/4); // assuming samples is integer power of 2 and greater than 16

  for (unsigned int i = 0; i < LSIZE; ++i)
  chess_prepare_for_pipelining
  {
    //8 MAC produce 4 partial output
    acc = readincr_v4(cascadein);
    buff.insert(2,readincr_v<4>(sig_in));
    acc = aie::sliding_mac<4,8>(acc,coe,0,buff,0);
    writeincr_v4(cascadeout,acc);

    acc = readincr_v4(cascadein);
    buff.insert(3,readincr_v<4>(sig_in));
    acc = aie::sliding_mac<4,8>(acc,coe,0,buff,4);
    writeincr_v4(cascadeout,acc);

    acc = readincr_v4(cascadein);
    buff.insert(0,readincr_v<4>(sig_in));
    acc = aie::sliding_mac<4,8>(acc,coe,0,buff,8);
    writeincr_v4(cascadeout,acc);

    acc = readincr_v4(cascadein);
    buff.insert(1,readincr_v<4>(sig_in));
    acc = aie::sliding_mac<4,8>(acc,coe,0,buff,12);
    writeincr_v4(cascadeout,acc);
  }
  delay_line = buff;
}
void fir_32tap_core2_init(){
  // Drop samples if not first block
  int const Delay = 16;
  for (int i = 0; i < Delay; ++i)
  {
    get_ss(0);
  }
  //initialize data
  for (int i=0;i<8;i++){
    int tmp=get_ss(0);
    delay_line.set(*(cint16*)&tmp,i);
  }
};

The last kernel code is as follows:

alignas(aie::vector_decl_align) static cint16 eq_coef3[8]={{49,50},{51,52},...};

//For storing data between graph iterations
alignas(aie::vector_decl_align) static aie::vector<cint16,16> delay_line;
__attribute__((noinline)) void fir_32tap_core3(input_stream<cint16> * sig_in, input_stream<cacc48> * cascadein,
      output_stream<cint16> * data_out){
  const aie::vector<cint16,8> coe = aie::load_v<8>(eq_coef3);
  aie::vector<cint16,16> buff = delay_line;
  aie::accum<cacc48,4> acc;
  const unsigned LSIZE = (SAMPLES/4/4); // assuming samples is integer power of 2 and greater than 16

  for (unsigned int i = 0; i < LSIZE; ++i)
  chess_prepare_for_pipelining
  {
    //8 MAC produce 4 output
    acc = readincr_v4(cascadein);
    buff.insert(2,readincr_v<4>(sig_in));
    acc = aie::sliding_mac<4,8>(acc,coe,0,buff,0);
    writeincr_v4(data_out,acc.to_vector<cint16>(SHIFT));

    acc = readincr_v4(cascadein);
    buff.insert(3,readincr_v<4>(sig_in));
    acc = aie::sliding_mac<4,8>(acc,coe,0,buff,4);
    writeincr_v4(data_out,acc.to_vector<cint16>(SHIFT));

    acc = readincr_v4(cascadein);
    buff.insert(0,readincr_v<4>(sig_in));
    acc = aie::sliding_mac<4,8>(acc,coe,0,buff,8);
    writeincr_v4(data_out,acc.to_vector<cint16>(SHIFT));

    acc = readincr_v4(cascadein);
    buff.insert(1,readincr_v<4>(sig_in));
    acc = aie::sliding_mac<4,8>(acc,coe,0,buff,12);
    writeincr_v4(data_out,acc.to_vector<cint16>(SHIFT));
  }
  delay_line = buff;
}
void fir_32tap_core3_init()
{
  // Drop samples if not first block
  int const Delay = 24;
  for (int i = 0; i < Delay; ++i){
    get_ss(0);
  }
  //initialize data
  for (int i=0;i<8;i++){
    int tmp=get_ss(0);
    delay_line.set(*(cint16*)&tmp,i);  
  }
};

The last kernel writes results to the output stream using acc.to_vector<cint16>(SHIFT).

Each kernel takes one cycle to produce a partial output. When they are working simultaneously, the system performance is one cycle to produce one output, which meets the design goal.

For more information about graph construction, stream broadcast, DMA FIFO insertion, profiling in simulation and hardware, design stall and deadlock analysis that may be met in system design, see AI Engine Tools and Flows User Guide (UG1076) .

Vectorized Version Using Multiple Kernels - 2023.2 English

AI Engine Kernel and Graph Programming Guide (UG1079)