Multiply-Accumulate processing element -- the classic systolic PE.
Ports
inputs: west => a, north => b
outputs: east => a, south => b, result => accThe MAC PE receives a value from its west neighbour and a value from its north neighbour, multiplies them, adds the product to an accumulator, and forwards both input values unchanged to the east and south respectively.
This is the exact PE used in the canonical systolic GEMM algorithm (Kung & Leiserson, 1979). Data flows west-to-east on the horizontal axis and north-to-south on the vertical axis; partial sums accumulate in-place at each PE.
State
The PE state is simply the accumulator value, defaulting to 0.
GraphBLAS connection
The MAC PE computes one entry of the semi-ring product C = A B where the semi-ring is `(multiply: , add: +)` over real numbers. GraphBLAS defines the same computation over arbitrary semi-rings.
Summary
Functions
Initializes the MAC PE with an optional initial accumulator.
Executes one MAC step: acc = acc + a * b; forwards a east and b south.
Types
@type state() :: number()
Functions
Initializes the MAC PE with an optional initial accumulator.
Examples
iex> ExSystolic.PE.MAC.init([])
0
iex> ExSystolic.PE.MAC.init(acc: 10)
10@spec step( state(), ExSystolic.PE.inputs(), non_neg_integer(), ExSystolic.PE.context() ) :: {state(), ExSystolic.PE.outputs()}
Executes one MAC step: acc = acc + a * b; forwards a east and b south.
When an input port is absent from the inputs map or has the value
:empty, it is treated as zero for accumulation and is NOT forwarded.
An explicit zero value (0) IS forwarded.
Examples
iex> {state, outputs} = ExSystolic.PE.MAC.step(0, %{west: 3, north: 4}, 0, %{})
iex> state
12
iex> outputs.east
3
iex> outputs.south
4
iex> outputs.result
12
iex> {state2, outputs2} = ExSystolic.PE.MAC.step(12, %{west: 2, north: 5}, 1, %{})
iex> state2
22
iex> outputs2.result
22