Definitions

Action

An action is something performed by a hardware unit. For example, a read or a compute.

Architecture

An architecture is the hardware that is running the workload. It describes the components that are available and how they are connected.

Component

A component is a hardware unit in the architecture. For example, a memory or a compute unit.

Dataflow

The order in which a mappings iterates over tiles, noting that tiles may be abstract before the mapping is fully defined.

Dataplacement

Which tile(s) are stored in each memory level of the accelerator, and for what time period, noting that tiles and time periods may be abstract before the mapping is fully defined.

Einsum

An Einsum is a computation step that executes using tensors. It includes two operations; map, which which is performed on combinations of values from its input tensors, and reduce, which combines mapped values into outputs. For example, a matrix multiplication Einsum uses a multiply operation for the map and a sum operation for the reduce.

Mapping

A mapping is a schedule that maps operations and data movement onto the hardware.

Loop

A loop is a bounded iteration over a rank variable with a given shape and/or pattern. Loops in AccelForge are the for loops in mappings.

Pmapping

A partial mapping, or pmapping, is a Mapping of a subset of the workload to the hardware.

Pmapping Template

A pmapping template is a template for a pmapping. It includes all storage nodes (dataplacement) and loop nodes (dataflow), but does not have loop bounds defined (tile shapes).

Rank

A rank is a dimension of a tensor.

Reuse

Reuse occurs when a piece of data is used used in multiple computations, but fetched fewer times from some memory. For example, we may fetch a piece of data from DRAM to on-chip memory once, then use it in ten computations. This would incur nine reuses of the piece of data.

Reuse Opportunity

Reuse opportunity is when a piece of data is used multiple times by the workload. It may or may not be turned into reuse if the hardware successfully leverages it.

Tensor

A tensor is a multi-dimensional array of data. Tensors are produced and consumed by Einsums. A tensor’s shape is parameterized by its ranks.

Tile

A subset of a tensor or operation space that is accessed by a set of loops in the mapping. If the loops are paratmeterized by variables for their bounds, then tile shapes are abstract.

Workload

A workload is a cascade of Einsums that are executed by the architecture. Einsums produce and consume tensors, which are exchanged between one another.