A Dynamic Programming Approach to Optimal Integrated Code Generation

1
A Dynamic Programming Approach to Optimal
Integrated Code Generation

• Christoph Keßler
• Andrzej Bednarski
• Linköping University (Sweden)

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Outline

• Code generation
• Our integrated approach
• Implementation and results
• Current and future work
• Conclusion

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Code Generation
IR-level Instruction scheduling
IR-level Reg. Alloc
IR-level Reg. Alloc
IR
IR-level Instruction scheduling
Instruction selection
Instruction selection
Instruction selection
Instruction selection
Target code
Target-level Instruction scheduling
Target-level Reg. Alloc
Target-level Reg. Alloc
Target-level Instruction scheduling
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Related Work

• Heuristics
• Optimal approaches
• ILP
• Dynamic programming
• Branch-and-bound
• Enumeration
• Constraint logic programming

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Integrated Code Generation
IR-level Instruction scheduling
IR-level Reg. Alloc
IR-level Reg. Alloc
IR
IR-level Instruction scheduling
Instruction selection
Instruction selection
Integrated Code generation
Instruction selection
Instruction selection
Target code
Target-level Instruction scheduling
Target-level Reg. Alloc
Target-level Reg. Alloc
Target-level Instruction scheduling
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Integrated Approach

• Christoph Keßlers previous work
• Scheduling by topological sorting
• Dynamic programming
• Selection DAG
• Time profile
• Extended selection DAG
• Basic block scope of code generation

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Topological Sorting
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Selection Tree
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Selection DAG

• Merge multiple instances of same zero indegree
  set z in one selection node
• Selection DAG
• Selection DAG is leveled in n1 levels
• Each schedule S corresponds to one path in the
  selection DAG

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Selection DAG
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Towards Time Optimization

• Machine model
• Generic superscalar/VLIW architecture
• Single/Multiple issue
• From IR level to target level
• Instruction selection
• Register allocation (homogenous)
• Imitate instruction dispatcher behaviour

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Time Profile

• Window of the instructions scheduled last for
  each unit that may still influence future
  scheduling decisions

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Extended Selection Node

• An extended selection node (z, t, P), summarizes
  all schedules of scheduled(z) that end with the
  time profile (t, P).
• Pruning (formal proof in the paper)

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Extended Selection DAG
Level 0
Level 1
Level 2
...
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Solution Space

• Group the extended selection nodes in each level
  according to execution time
• Construct solution space in order of increasing
  time
• Postpones the combinatorial explosion

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Implementation

• C
• LEDA
• XML based architecture description language
• LCC as Cfront-end

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Results Random DAGs
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Results Random DAGs
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Results FIR Filter
Basic Block DAG nodes Time archi. 1 Time archi. 2
BB1 16 3.5s 4.0s
BB2 16 8.0s 9.5s
BB3 30 32150.2s 44044.9s
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Results Matrix Multiplication
Basic Block DAG nodes Time archi. 1 Time archi. 2
BB2 30 105.0s 141.8s
BB2 (unrolled) 40 608.5s 947.2s
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Results Jacobi Grid Relax.
Basic Block DAG nodes Time archi. 1 Time archi. 2
Loop body (5) 40 115.8s 131.8s
Loop body (9) 53 13613.2s 20051.5s
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Current and Future Work

• Time-space profile for irregular register sets
• Speculative instruction selection
• Extensions of architecture description language
• Beyond basic block level
• Time-space profiles as connector descriptions

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Conclusion

• Goal fully integrated code generation
• Dynamic programming approach
• Time profiles to compress the solution space
• Improved order of solution space construction
• Feasible for medium sized basic blocks
• Potential for extensions
• Alternative to ILP
• Home page www.ida.liu.se/chrke/optimist