Lookup Tables - 2023.2 English - UG1529

Note

Linear approximation functionality is only available from AIE-ML

Type to support a linear approximation via interpolation with slope/offset values stored in a lookup table.

The offset values are simply the samples of the function to be approximated. The slope values, which are the slopes of the function at the corresponding sample, are used in conjunction with the input to more accurately estimate the function value between sample points.

The logical steps of the computation for an integer based linear approximation are:

• index = (input >> step_bits) + bias
• slope/offset pair read from LUT based on index
• output = slope * (input & ((1 << step_bits) - 1)) + (offset << shift_offset)

while the steps for a floating point based approximation are:

• index = (int(floor(input)) >> step_bits) + bias
• slope/offset pair read from LUT based on index
• output = slope * input + offset

Note that for integer based linear approximations, the slope is multiplied by an integer value in the range [0, 1 << step_bits) and therefore tweaking of the LUT values or linear_approx parameters may be required to ensure that offset[i] + slope[i] * ((1 << step_bits) - 1) approximately equals offset[i+1].

The slope and offset values are expected to be placed adjacent in memory. The number of achieved lookups per cycle is determined by the aie::lut object that encapsulates the contents of the lookup table. The following example shows the memory layout of a 128b bank width lookup table with 16b values and slopes, which achieves 4 lookups per cycle:

Note that while the floating point linear approx requires the offset data to be 32b floats, the slope data is required to be bfloat16. However, it is required that all values in the LUT be 32b to ensure the LUT is correctly aligned. While it is safe to use floats as the storage type for the lookup table, it is required that the low 16 mantissa bits of the floating point slope value be zero.

Template Parameters

T	Type of the input vector, containing values used to index the lookup table.
MyLUT	Definition of the LUT type, using the lut type.

Abstraction to represent a LUT that is stored in memory, instantiated with pointer(s) to the already appropriately populated memory and the number of elements.

The requirement on memory layout is that for degree N parallel accesses, N copies of the LUT data are required; i.e.

• For a single load without parallelism, the values required to be stored linearly in memory.
• For 2 loads in parallel, the LUT needs to have 2 copies of the LUT values with repetition every bank width. For example with 32b values and a 128b bank width, in memory we would have the first 4 values (128b), then the same 4 again, then the next 4, which then repeat, etc.
• For 4 loads in parallel, we require the same layout as for 2 loads, but two distinct copies in this layout, placed in different memory banks.

Currently the only supported implementation on this architecture is for 4 parallel accesses.

Template Parameters

ParallelAccesses	Defines how many parallel accesses will be done in a single LUT access, possibilities depend on the hardware available for the given architecture
OffsetType	Type of values stored within the lookup table.
SlopeType	Optional template parameter, only needed in certain cases of linear approximation where the offset/slope value pair uses two different types.

Note

Parallel lookup functionality is only available from AIE-ML

Type with functionality to directly index a LUT based on input vector of values. The number of achieved lookups per cycle is determined by the aie::lut object that encapsulates the contents of the lookup table. Refer to aie::lut for more details.

Real signed and unsigned integer types (>=8b) are supported as indices. All types (>=8b) are supported as value types, including bfloat16, real, and complex types.

Note

8b value type lookups require the data to be stored in the lookup tables as 16b values due to the granularity of the memory accesses.

Template Parameters

T	Type of the input vector, containing values used to index the lookup table.
MyLUT	Definition of the LUT type, using the lut type
oor_policy	Defines the "out of range policy" for when index values on the input go beyond the size of the LUT. It can either saturate, taking on the min/max valid index, or truncate, retaining the lower bits for unsigned indicies or wrapping in the interval [-bias,lut_size-bias) for signed indices. Saturating is the default behaviour, but for certain non-linear functions which repeat after an interval truncation may be required.