ILPc: A novel approach for scalable timing analysis of synchronous programs Hugh Wang Partha S. Roop Sidharta Andalam

Outline Timing analysis of concurrent programs Problem statement Our approach - ILPc Results Conclusions

Acronyms ILP – Integer Linear Program ILPs – ILP sequential ILPc – ILP concurrent EOT = End of Tick – also known as “pause” TCCFG – Timed concurrent control flow graph (Intermediate format)

Synchronous languages abort [loop foo1(); pause; foo2(); pause; end loop ] || [loop foo3(); pause; foo4(); pause; end loop ] when s

Synchronous languages abort [loop foo1(); pause; foo2(); pause; end loop ] || [loop foo3(); pause; foo4(); pause; end loop ] when s

Synchronous languages abort [loop foo1(); pause; foo2(); pause; end loop ] || [loop foo3(); pause; foo4(); pause; end loop ] when s abort start abort end

Synchronous languages abort [loop foo1(); pause; foo2(); pause; end loop ] || [loop foo3(); pause; foo4(); pause; end loop ] when s abort condition

Synchronous languages abort [loop foo1(); pause; foo2(); pause; end loop ] || [loop foo3(); pause; foo4(); pause; end loop ] when s abort condition False True

Synchronous languages abort [loop foo1(); pause; foo2(); pause; end loop ] || [loop foo3(); pause; foo4(); pause; end loop ] when s fork

Synchronous languages abort [loop foo1(); pause; foo2(); pause; end loop ] || [loop foo3(); pause; foo4(); pause; end loop ] when s

Synchronous languages abort [loop foo1(); pause; foo2(); pause; end loop ] || [loop foo3(); pause; foo4(); pause; end loop ] when s

Synchronous languages Time Read Inputs Emit outputs Computation

Synchronous languages Time Tick 1Tick 4Tick 2Tick 3

Synchronous languages Time Worst Case Reaction Time analysis ◦ WCRT analysis Synchrony hypothesis ◦ Reactive system operates infinitely fast compared to the environment. Validation ◦ Min(inter-arrival-time of events) > Max (Reaction Time) Longest tick

Outline Timing analysis of concurrent programs Problem statement Our approach - ILPc Results Conclusions

Motivating example A1 A2 A3 T1 B1 B2 T2 C1 C2 T3 T1 || T2 || T3

Motivating example A1 A2 A3 T1 B1 B2 T2 C1 C2 T Execution Time: 25

Motivating example A1 A2 A3 T1 B1 B2 T2 C1 C2 T Execution Time: 28

Motivating example A1 A2 A3 T1 B1 B2 T2 C1 C2 T Execution Time: 35

Conventional approaches Max-plus M. Boldt and C. Traulsen and R. Hanxleden. Worst Case Reaction Time Analysis of Concurrent Reactive Programs. ENTCS, 203(4), L. Ju, B. K. Huynh, A. Roychoudhury, and S. Chakraborty. Performance debugging of Esterel specifications. CODES-ISSS 2008.

Conventional approaches State exploration L. Ju, B. K. Huynh, S. Chakraborty, and A. Roychoudhury. Context- sensitive timing analysis of Esterel programs. DAC, S. Andalam, P. S. Roop, and A. Girault. Pruning infeasible paths for tight WCRT analysis of synchronous programs. DATE, M. Kuo, R. Sinha, and P. S. Roop. Efficient WCRT analysis of synchronous programs using reachability. DAC, ILPs Model checking Reachability

Motivating example A1 A2 A3 T1 B1 B2 T2 C1 C2 T WCRT analysis -Max-Plus WCRT = Max(T1) + Max(T2) + Max(T3) = A3 + B1 + C2 = = 40 cycles -State Exploration A1+B1+C1 = 25 A2+B2+C2 = 28 A3+B1+C1 = 35 A1+B2+C2 = 23 A2+B1+C1 = 30 A3+B2+C2 = 33 WCRT = Max(25,28,35,23,30,33) = 35 cycles

Tradeoff Precision Analysis Time Max-plus State exploration

Motivating example A1 A2 A3 T1 B1 B2 T2 C1 C2 T

Motivating example A1 A2 A3 T1 B1 B2 T2 C1 C2 T WCRT analysis -Max-Plus WCRT = Max(T1) + Max(T2) + Max(T3) = A3 + B2 + C2 = = 45 cycles -State Exploration A1+B1+C1 = 25 A2+B2+C2 = 40 A3+B1+C1 = 35 A1+B2+C2 = 35 A2+B1+C1 = 30 A3+B2+C2 = 45 WCRT = Max(25,40,35,35,30,45) = 45 cycles

The problem statement Precision Analysis Time Max-plus State exploration

Our approach Our approach (ILPc) ◦ Inspired by counter example guided model checking ◦ Also has some ideas similar to local model checking Success Fail

Outline Timing analysis of concurrent programs Problem statement Our approach - ILPc Results Conclusions

Overview of ILPc TCCFGILP model

E1 E2 E5 E4 E3 E6 E7 E12 E11E8 E9 E10 E17 E13 E14 E15 E16

ILP model E1 E2 E5 E4 E3 E6 E7 E12 E11E8 E9 E10 E17 E13 E14 E15 E16

ILP model E1 E2 E5 E4 E3 E6 E7 E12 E11E8 E9 E10 E17 E13 E14 E15 E16

ILP Compared with the conventional ILP ◦ Directly capture features of synchronous languages. ◦ More precise WCRT estimates with minimum overhead.

Overview of ILPc TCCFGILP model Tick expressions

Tick Expressions 0 (1,3,5…)

Overview of ILPc ILP solver TCCFG Ticks can be aligned? ILP model Tick expressions WCRT & Execution path

Verifying tick alignment 0

Overview of ILPc ILP solver TCCFG Ticks can be aligned? ILP model Tick expressions WCRT & Execution path Refinement Success Fail

Outline Timing analysis of concurrent programs Problem statement Our approach - ILPc Results Conclusions

Benchmarking Compared with 3 existing approaches [1,2,3] Conducted in 2 phases ◦ Phase 1: Theoretical performance ◦ Phase 2: Real-world applications Benchmark computer ◦ Windows based ◦ Quad-core 1.6 GHz CPU ◦ 8 GB memory [1] L. Ju, B. K. Huynh, S. Chakraborty, and A. Roychoudhury. Context- sensitive timing analysis of Esterel programs, DAC, [2] S. Andalam, P. S. Roop, and A. Girault. Pruning infeasible paths for tight WCRT analysis of synchronous programs, DATE [3] M. Kuo, R. Sinha, and P. S. Roop. Efficient WCRT analysis of synchronous programs using reachability, DAC, 2011.

Scalability Analysis time vs. program states. Analysis time of ILPc ◦ Time taken for each iteration.  Number of program states. ◦ The number of iteration.  Structure and cost distribution.

Benchmarking: Phase 1 Two sets of benchmarks ◦ Set A - Maximum number of required iterations to find the WCRT. ◦ Set B - Minimum number of required iterations to find the WCRT. (Iteration = 1)

Benchmarking: Phase 1 Set A A1 A2 End … 5 0

Benchmarking: Phase … Set A A1 A2 End Set B …

Benchmarking: Phase 1 Set A

Benchmarking: Phase 1 Set B

Benchmarking: Phase 1 Same precision. Analysis time of ILPc depends heavily on the number of iterations rather than the number of program states. On average, analysis time of ILPc should be between the worst case and best case scenarios.

Benchmarking: Phase2 NameWCRTThreads 1ChannelProtocol9977 2Flasher6177 3RobotSonar DrillStation CruiseControl RailroadCrossing WaterMonitor Small Large L. H. Yoong and G. D. Shaw. Auckland function block benchmark. University of Auckland,

Benchmarking: Phase2 Benchmarks 1-4 (less than 20 threads)

Benchmarking: Phase2 Benchmarks 5-7 (more than 20 threads) >1 hr Out of Memory

Benchmarking: Phase2

Results summary Same precision as state exploration approaches. Orders of magnitude faster compared to state exploration approaches for synchronous benchmarks for industrial automation applications.

Conclusions We proposed ILPc tailored for timing analysis of concurrent programs. ILPc paves the way for scalable timing analysis through an iterative refinement process. Future work: ◦ Consideration of complex architectural features. ◦ ILPc variant for the analysis of parallel programs.

Thank you!