Multiple Lanes Multiplication - sliding_mul - 2024.2 English - UG1079

AI Engine Kernel and Graph Programming Guide (UG1079)
Document ID
UG1079
Release Date
2024-11-28
Version
2024.2 English

AI Engine provides hardware support to accelerate a type of multiple lanes multiplication, called sliding multiplication. It allows multiple lanes to do MAC operations simultaneously, and the results are added to an accumulator. It especially works well with (but not limited to) finite impulse response (FIR) filter implementations.

These special multiplication structures or APIs are named aie::sliding_mul*. They accept coefficient and data inputs. Some variants of aie::sliding_mul_sym* allow pre-adding of the data input symmetrically before multiplication. These classes include:

  • aie::sliding_mul_ops
  • aie::sliding_mul_x_ops
  • aie::sliding_mul_y_ops
  • aie::sliding_mul_xy_ops
  • aie::sliding_mul_sym_ops
  • aie::sliding_mul_sym_x_ops
  • aie::sliding_mul_sym_y_ops
  • aie::sliding_mul_sym_xy_ops
  • aie::sliding_mul_sym_uct_ops

For more information about these APIs and supported parameters, see the AI Engine API User Guide (UG1529).

For example, the aie::sliding_mul_ops class provides a parametrized multiplication that implements the following compute pattern.

DSX = DataStepX
DSY = DataStepY
CS = CoeffStep
P = Points
L = Lanes
c_s = coeff_start
d_s = data_start 
out[0] = coeff[c_s] * data[d_s + 0] + coeff[c_s + CS] * data[d_s + DSX] + ... + coeff[c_s + (P-1) * CS] * data[d_s + (P-1) * DSX]
out[1] = coeff[c_s] * data[d_s + DSY] + coeff[c_s + CS] * data[d_s + DSY + DSX] + ... + coeff[c_s + (P-1) * CS] * data[d_s + DSY + (P-1) * DSX]
...
out[L-1] = coeff[c_s] * data[d_s + (L-1) * DSY] + coeff[c_s + CS] * data[d_s + (L-1) * DSY + DSX] + ... + coeff[c_s + (P-1) * CS] * data[d_s + (L-1) * DSY + (P-1) * DSX]
Table 1. Template Parameters
Parameter Description
Lanes Number of output elements.
Points Number of data elements used to compute each lane.
CoeffStep Step used to select elements from the coeff register. This step is applied to element selection within a lane.
DataStepX Step used to select elements from the data register. This step is applied to element selection within a lane.
DataStepY Step used to select elements from the data register. This step is applied to element selection across lanes.
CoeffType Coefficient element type.
DataType Data element type.
AccumTag Accumulator tag that specifies the required accumulation bits. The class must be compatible with the result of the multiplication of the coefficient and data types (real/complex).

The following figure shows how to use the aie::sliding_mul_ops class and its member function, mul, to perform the sliding multiplication. It also shows how each parameter corresponds to the multiplication.

Figure 1. sliding_mul_ops Usage Example

Besides the aie::sliding_mul* classes, AI Engine API provides aie::sliding_mul* functions to do sliding multiplication and aie::sliding_mac* functions to do sliding multiplication and accumulation. These functions are simply helpers, that use the aie::sliding_mul*_ops classes internally and are provided for convenience. These include:

  • aie::sliding_mul
  • aie::sliding_mac
  • aie::sliding_mul_sym
  • aie::sliding_mac_sym
  • aie::sliding_mul_antisym
  • aie::sliding_mac_antisym
  • aie::sliding_mul_sym_uct
  • aie::sliding_mac_sym_uct
  • aie::sliding_mul_antisym_uct
  • aie::sliding_mac_antisym_uct

The following examples perform asymmetric sliding multiplications (template prototypes are in comments for quick reference).

constexpr unsigned Lanes = 8, Points = 8;
constexpr unsigned CoeffStep = 1;
constexpr unsigned DataStepX = 1, DataStepY = 1;
using CoeffType = int16;
using DataType = int16;
using AccumTag = acc48;

aie::vector<int16,16> va;
aie::vector<int16,64> vb0,vb1;
aie::accum<acc48,8> acc = aie::sliding_mul_ops<Lanes, Points, CoeffStep, DataStepX, DataStepY, CoeffType, DataType, AccumTag>::mul(va, 0, vb0, 0);
acc = aie::sliding_mul_ops<Lanes, Points, CoeffStep, DataStepX, DataStepY, CoeffType, DataType, AccumTag>::mac(acc, va, 8, vb1, 0);
auto vout=acc.to_vector<int32>(15);

constexpr unsigned coeff_start = 0;
constexpr unsigned data_start = 0;
aie::vector<int32,32> data_buff;
aie::vector<int32,8> coeff_buff;
aie::accum<acc80,8> acc_buff = aie::sliding_mul<Lanes, Points>(coeff_buff, coeff_start, data_buff, data_start);

Following are symmetric sliding multiplication examples.

constexpr unsigned Lanes = 4, Points = 16;
constexpr unsigned CoeffStep = 1;
constexpr unsigned DataStepX = 1, DataStepY = 1;
using CoeffType = int16;
using DataType = cint16;
using AccumTag = cacc48;
constexpr unsigned coeff_start=0;
constexpr unsigned data_start=0;

aie::vector<cint16,16> data_buff;
aie::vector<int16,8> coeff_buff;
auto acc_buff = aie::sliding_mul_sym_ops<Lanes, Points, CoeffStep, DataStepX, DataStepY, CoeffType, DataType, AccumTag>::mul_sym(coeff_buff, coeff_start, data_buff, data_start);

auto acc_buff2 = aie::sliding_mul_sym<Lanes, Points, CoeffStep, DataStepX, DataStepY>(coeff_buff, coeff_start, data_buff, data_start);

constexpr unsigned ldata_start=0;
constexpr unsigned rdata_start=8;
aie::vector<cint16,16> ldata,rdata;
aie::vector<int16,8> coeff;
// symmetric sliding_mul using two data registers
auto acc = aie::sliding_mul_sym<Lanes, Points/2, CoeffStep, DataStepX, DataStepY>(coeff, coeff_start, ldata, ldata_start, rdata, rdata_start);
Note: All registers in sliding multiplication must be considered circular. They go back to the start after they reach the end.

The following figures show how the previous symmetric examples are computed.

Figure 2. sliding_mul_sym_ops Usage Example
Figure 3. sliding_mul_sym Function with Two Data Registers

Considerations When Using sliding_mul

Some restrictions include:

  • Data width <=1024 bits, and Coefficient width <=256 bits
  • Lanes * Points >= MACs per cycle for that type
  • int8 is not supported in sliding_mul_sym_ops and sliding_mul_sym_uct_ops.