First Principles for Multidimensional Array Data

First Principles for Multidimensional Array Data

Codomain

• The codomain element space is a subset of elements residing within a contiguous span of memory.
• Elements are (typically) of the same type and in-memory representation.

Domain

• The domain index space is a Cartesion product of integer ranges.
• Index ranges are (typically) dense.
• The number of integer ranges is the rank of the domain index space.

Layout

• The layout is a mapping from the domain index space to the codomain element space.
• A layout mapping is (typically) an O(rank) computation.
  • Common rank-2 layout mappings are row major and column major.
• A layout mapping is typically, but not required to be, injective.

License (definition: permission or freedom to act)

• A computation may have a temporary license to operate on the codomain of a multidimensional array
• Read (const): computation does not modify elements
• Read-volatile: computation does not modify elements with expectation that elements are concurrently modified
• Read-restrict: computation does not modify elements with guarantee that elements are not modified
• Write: computation modifies elements
• Write-volatile: computation modifies elements with expectation that elements are concurrently read
• Write-restrict: computation claims exclusive access to elements for modification
• Write-atomic: computation modifies elements with expectation that elements are concurrently modified

Locality

• Characterization of a computations' accesses to elements with respect to the location(s) of those elements in memory
• Dependent upon computations' scheduling and patterns in execution resources, and elements' scheduling and layout in memory resources