Domain Library

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Domain Library
Imran Haque http//titanium.cs.berkeley.edu U.C.
Berkeley September 9, 2004
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Outline

• Motivation for Domains
• Overview of the Domain library
• Upgrades to the Domain library
• Language-level changes
• Compiler changes
• Implementation improvements

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Titanium Arrays (Grids)

• Designed for grid computation
• Computing arbitrary-width ghost regions for
  high-order solvers
• Support relaxation operators that work on every
  other element or on array interior
• Expressive
• Rectangular subarrays are also arrays
• Index sets are first-class concepts
• Modify index sets to produce aliased arrays

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Domains overview

• RectDomains live in N-dimensional discrete
  space
• Prior Experience Generality can be powerful, but
  also slow so dont pay for unnecessary features
• RectDomainltNgt N-dimensional hyper-rectangle
• DomainltNgt arbitrary collection of points in
  N-space

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Domain library features

• Strides
• Set operations
• Manipulation operations
• Size modification, translation

Unit-stride
2-stride
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Domains example
double 2d gridnew double-5,-55,5 grid.s
et(0.0) double 2d transpgrid.permute(2,1) D
omainlt2gt dom1,12,23,37,7 foreach
(p in (grid.domain()dom))
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Motivation for Domain upgrades

• Domain library recognized as performance barrier
  in applications work
• AMR project
• Applications primarily using unit stride

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Language and compiler changes

• Language
• Domains as Objects
• Naming changes
• Increased arity (formerly limited to 3d)
• Code generation
• Optimized construction

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Implementation - RectDomain

• RectDomain
• Internal representation
• 25 less data, 2.5-6.5 speed boost
• Faster representation of the empty set
• Unit-stride optimizations
• Intersections are 2-3x faster
• other algorithms
• size() 20-40 faster
• Subset testing 20-40 faster

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Implementation - Domain

• Domain
• isRectangular
• 4-50x faster
• boundingBox
• 2x faster
• Internal representation (planned)
• Transition from linked list to simple array
• Caching of query values

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Benchmarking Notes

• All benchmarks performed on a single-CPU Pentium
  4 system running Linux 2.4.22 (Fedora Core 1)
• tc command-line options
• Narrow backend -O nobcheck verbose tc-flags
  -Onoinline
• Wide backend -O nobcheck verbose tc-flags
  -Onoinline backend udp-cluster-uniprocess
• Runtime options
• Narrow backend defaults
• Wide backend TI_SPAWNFNL, spawning 1 process