Compiletime Composition of Runtime Data and Iteration Reorderings

1
Compile-time Composition of Run-time Data and
Iteration Reorderings

• Michelle Mills Strout
• Larry Carter
• Jeanne Ferrante

2
Background

• Why reordering?
• Data locality
• Parallelism
• Run-time Reordering
• Inspector
• Executor

3
Techniques

• Data Reordering
• CPACK, gPart
• Iteration Reordering
• lexGroup, bucket tiling, lexSort
• Sparse Tiling
• FST, cache Blocking

4
Motivation

• Apply multiple optimizations
• Verified by experiments
• Challenges
• How to carry out one by one ()
• Which to apply
• Order
• Automated ???

5
Current Situation

• Restricted to affine loops
• Uniform representation
• Composition of optimizations
• Legality
• Conservative on non-affine refs

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Possible Solution

• Formalize the data mapping
• Formalize the dependences
• the effect of transformation
• Changes on mappings and dependences
• Apply one by one
• Final data movement

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Original data and iteration
Composed inspector
executor
Transform(1)
Data Movement
Transform(2)
Reordered data and iterations
Data Mapping Dependences (1)
Data Mapping Dependences (2)
Data Mapping Dependences (3)
Compiler ??
Original Code
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Formalization

• Loop space
• Pair ltstatement, loop idgt
• (lt,gtlt,gtlt,gt)
• Data mapping
• Point in loop space ? data referenced
• Dependences
• Point in loop space ? Point in loop space

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Transformations

• Data Reordering Ra?a
• Affect data mapping
• Iteration Reordering TI?I
• Affect data mapping and dependences
• Legality lexicographical order
• Sparse Tiling combination of two
• Splitting loops larger loop space.

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Experiment Results

• Oops! No experiment results