Domain-Specific Languages for Stencil Computations - Mathematics ...
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Domain-Specific Languages for Stencil Computations - Mathematics ...
Finite-‐difference stencils are very common in numerical modeling. ... Stencil
panern determines the interacVon among points ... 65 66 101 102 133 134. 00
00.
Domain-Specific Languages for Stencil Computations Azamat Mametjanov Boyana Norris Mathema4cs and Computer Science Division Argonne Na4onal Laboratory
CACHE-2012 Annual Meeting, December 6-7, 2012
Motivation
q
q
Finite-‐difference stencils are very common in numerical modeling. They exhibit high degree of data parallelism and regular structure. However, their memory requirements hinder the performance. Our approach consists of – – – –
Exploita4on of a stencil’s data access paOern Automa4c conversion of C loops to CUDA C host+kernel code Automa4c tuning of CUDA C performance parameters Raising the programming model to domain abstrac4ons
2
Outline
q q q q q q
Introduc4on Stencil data structures Transforma4on and tuning framework of Orio Our approach Results DSLs for stencils
3
Stencils
q q
Sets of neighboring discrete points in a structured grid Stencil paOern determines the interac4on among points – – – –
Domain dimension: 1D, 2D, 3D Stencil shape: star, box Stencil width: distance from stencil center Boundary condi4on: Dirichlet, periodic etc.
4
Grid, adjacency matrix and its compression -‐3
Grid Element
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29 30 65 66
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101 102 133 134
31 32 67 68
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135 136
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103 104 135 136
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105 106
137 138
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105 106 137 138
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35 36
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107 108
139 140
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107 108 139 140
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(a)
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-‐1
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25 26 61 62 97 98 2
1
(b)
(c)
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Outline
q q q q q q
Introduc4on Stencil data structures Transforma2on and tuning framework of Orio Overview of the approach Results DSLs for stencils
6
Method: Code Transformation q
Mo4va4on – Compila4on: HL source code into LL portable executable code – Op4miza4on: performance, energy – Refactoring: resiliency, maintainability, readability
q
Workflow – – – –
q
Parse: any structured source text into abstract syntax tree Analyze: common intermediate representa4on Transform: composi4ons of reusable transforms Generate: any structured target text
Challenges – Create source and target domains – Create analysis and transforma4on rules 7
Method: Code Tuning q
Mo4va4on – Deep component stacks – Each component is adjustable
q
Workflow – – – –
q
System model: pre-‐specified, learned Applica4on profile: memory-‐/compute-‐bound Configure: create a valid configura4on of parameters Select: the best performing parameter configura4on
