AI Engine provides hardware support to accelerate a type of multiple lanes multiplications, 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]
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.
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).
/*template<unsigned Lanes, unsigned Points, int CoeffStep, int DataStepX, int DataStepY, ElemBaseType CoeffType, ElemBaseType DataType, AccumElemBaseType AccumTag = detail::default_accum_tag_t<CoeffType, DataType>>
struct aie::sliding_mul_ops< Lanes, Points, CoeffStep, DataStepX, DataStepY, CoeffType, DataType, AccumTag >
template<VectorOrOp VecCoeff, VectorOrOp VecData>
static constexpr accum_type mul (const VecCoeff &coeff, unsigned coeff_start, const VecData &data, unsigned data_start)
*/
aie::vector<int16,16> va;
aie::vector<int16,64> vb0,vb1;
aie::accum<acc48,8> acc = aie::sliding_mul_ops<8, 8, 1, 1, 1, int16, int16, acc48>::mul(va, 0, vb0, 0);
acc = aie::sliding_mul_ops<8, 8, 1, 1, 1, int16, int16, acc48>::mac(acc, va, 8, vb1, 0);
window_writeincr(out,acc.to_vector<int32>(15));
/*template<unsigned Lanes, unsigned Points, int CoeffStep = 1, int DataStepX = 1, int DataStepY = DataStepX, AccumElemBaseType AccumTag = accauto, VectorOrOp VecCoeff = void, VectorOrOp VecData = void>
auto sliding_mul (const VecCoeff &coeff, unsigned coeff_start, const VecData &data, unsigned data_start)
*/
aie::vector<int32,32> data_buff;
aie::vector<int32,8> coeff_buff;
aie::accum<acc80,8> acc_buff = aie::sliding_mul<8, 8>(coeff_buff, 0, data_buff, 0);
Following are symmetric sliding multiplication examples.
/*template<unsigned Lanes, unsigned Points, int CoeffStep, int DataStepX, int DataStepY, ElemBaseType CoeffType, ElemBaseType DataType, AccumElemBaseType AccumTag = detail::default_accum_tag_t<CoeffType, DataType>>
struct aie::sliding_mul_sym_ops<Lanes, Points, CoeffStep, DataStepX, DataStepY, CoeffType, DataType, AccumTag >
template<VectorOrOp VecCoeff, VectorOrOp VecData>
static constexpr accum_type mul_sym (const VecCoeff &coeff, unsigned coeff_start, const VecData &data, unsigned data_start)
*/
aie::vector<cint16,16> data_buff;
aie::vector<int16,8> coeff_buff;
auto acc_buff = aie::sliding_mul_sym_ops<4, 16, 1, 1, 1, int16, cint16, cacc48>::mul_sym(coeff_buff, 0, data_buff, 0);//usage 1
/*template<unsigned Lanes, unsigned Points, int CoeffStep = 1, int DataStepX = 1, int DataStepY = DataStepX, AccumElemBaseType AccumTag = accauto, VectorOrOp VecCoeff = void, VectorOrOp VecData = void>
auto sliding_mul_sym (const VecCoeff &coeff, unsigned coeff_start, const VecData &data, unsigned data_start)
*/
auto acc_buff2 = aie::sliding_mul_sym<4, 16, 1, 1, 1>(coeff_buff, 0, data_buff, 0);//usage 2: equivalent to above
/*template<unsigned Lanes, unsigned Points, int CoeffStep = 1, int DataStepX = 1, int DataStepY = DataStepX, AccumElemBaseType AccumTag = accauto, VectorOrOp VecCoeff = void, VectorOrOp VecData = void>
auto sliding_mul_sym (const VecCoeff &coeff, unsigned coeff_start, const VecData &ldata, unsigned ldata_start, const VecData &rdata, unsigned rdata_start)
*/
aie::vector<cint16,16> ldata,rdata;
aie::vector<int16,8> coeff;
auto acc = aie::sliding_mul_sym<4, 8, 1, 1, 1>(coeff, 0, ldata, 0, rdata, 8);//symmetric sliding_mul using two data registers.
The following figures show how the previous symmetric examples are computed.
Considerations When Using sliding_mul
- Data width <=1024 bits, and Coefficient width <=256bits
- Lanes * Points >= (MACs per cycle for that type)
- int8 is not supported