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S T A R S

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S T A R S

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  1. STatic Analysis of Reactive Systems S T A R S Felice Balarin Cadence Berkeley Labs

  2. Discrete System Example • For a given processor, can I process all workload between two ticks? • How much bus traffic will I generate? • How much energy will I use? Voice Mail Pager play tick network request sample control buffer message frame

  3. Solutions • Prototyping • expensive, comes very late in the design cycle • Simulation • limited number of test vectors • need estimates on timing, energy, bus traffic, ... • STARS: STatic Analysis of Reactive Systems • valid upper bound for any input

  4. STARS A methodology for worst-case analysis of discrete systems that can be used to find a conservative bound on response time. • and power • and bus utilization

  5. Busy Busy VM pager Timing Analysis • STARS gives an upper bound on processor busy period for ANY input sequence play tick network request sample control buffer message frame buffer control Idle

  6. Outline • STARS theory • simple • timing • VCC implementation • Automatic abstraction

  7. play frame tick SIGNATURE pl tk Fenv rq sm pl = 1 fr = 2 tk = 3 Fcntr Fbfr ms fr SIGNATURE ABSTRACTION STARS overview • given T find s that is worse than signature of any execution window of length T • let T be time required to process inputs with signature s play tick network request sample control buffer message frame

  8. Signatures • in practice, counting “events” • state transitions may be considered events • combinations of events may have separate counters • may need linear constraints over counters • less events is “better than” () more events

  9. system t t+T t t+T q = exists F s,T F( s, T) Signature Abstractions Estimate output signature based on input signature and length • must be conservative (ideally, not more than necessary) 

  10. Signature Abstraction: Practice Different approaches for • environment • mostly manual • useful for simulation test-benches, formal verification, ... • depends mostly on time • system • need to analyze code • could be automated for restricted class of systems • mostly depends on signatures

  11. Signature Abstractions: Environment • at least 625s between messages • Fms (s, T) = T/625 + 1 • tick has 125s period • Ftk (s, T) = T/125 + 1 • at most 1 play a second • Fpl (s, T) = T/1,000,000 + 1 play tick network request sample control buffer message frame

  12. Signature Abstraction: Buffer BUFFER: if ( present ( frame ) { samples = frame; last = 50; } if ( present ( tick ) && last > 0) { emit sample ( samples[ last -- ] ); if ( last == 20 ) emit request(); } play tick network request sample control buffer message frame Frq (s, T) = min( fr, tk/30) Fsm (s, T) = min( tk, 50*fr )

  13. t t+T Fix-point Theorem If: • s = F(s, T), • s is worse than signature of initial state, then s is worse than signature of any execution segment of length T  s

  14. Solving Fix-Point Equations Simple iteration lets be the signature of initial state repeat s = F (s, T) until convergence works because F is monotone, so s either converges, or grows beyond any reasonable bounds

  15. s  W(s) Task 2 Task 1 Idle Workload Function Estimates required processor time from signatures • must be conservative

  16. Workload Function: VM pager BUFFER: if ( present ( frame ) { samples = frame; last = 50; } if ( present ( tick ) && last > 0) { emit sample ( samples[ last -- ] ); if ( last == 20 ) emit request(); } play tick network request sample control buffer message frame 1 line = 10 time units W(s) = 20*fr + 20*sm + ...

  17. STARS • Pick a signature • Chose a signature abstraction F and workload function W and verify they and conservative • Solve s = F(s,T) T = W(s) • Tis a bound on response time the processor cannot be continuously busy for more than T time units

  18. (More) Realistic Voice Mail Pager • 16 modules • ~ 4000 lines of C++ code annotated with timing estimates • build signature abstractions manually • 150 lines of C code

  19. VMP First experiment • model environment so that a single message is received and then played • same as DES test-bench • max busy period: • DES: 82 s(simulating 8s took ~ 30 s) • STARS: 83 s(took 16 ms to compute)

  20. 50x125 125 1 2 3 29 30 31 49 50 message, play VMP second experiment • same as first except: • don’t limit the environment to a single message • max busy period: • STARS 148 s (more than 125 s between two ticks) • DES: can find input that has 146 s 66s wide window in a 6250 s period

  21. Outline • STARS theory • simple • timing • VCC implementation • Automatic abstraction

  22. VCC • FUNCTION • a network of communicating processes • ARCHITECTURE • processors, ASICs, buses, memories • MAPPING • allows performance estimation Functional simulation, Performance analysis Export to implementation, STatic Analys

  23. VCC Function Specification • Black Box C++ • can emit events on output ports • can detect events on input ports • Init() function executed once at the beginning • Run() function can be executed if there are some input events can be simulated cannot be estimated

  24. VCC Function Specification • White Box C • point_entry_init() instead of Init() • point_entry_run() instead of Run() can be converted to Black Box and simulated can be estimated, converted to Black Box annotated with performance estimates and simulated

  25. Extended Black Box for STARS • there is a counter counting the number of events on each port • the user can define additional counters • add starsAbstraction() to Init() and Run() • starsAbstraction() is used by STARS • starsAbstraction() can be verified by executing it during the simulation using monitors

  26. How it fits in VCC (black.h) #include "black_interface.h" // generated by "fabricate" #ifndef _black_h_ #define _black_h_ class CPP_MODEL_IMPLEMENTATION : public CPP_MODEL_INTERFACE { public: CPP_MODEL_IMPLEMENTATION(const ModuleProto &, InstanceInit &); void Run(); void Init(); ... starsCounter incount; void starsAbstraction(); }; #endif ...

  27. How it fits in VCC (black.cpp) #include "black.h" #include <assert.h> CPP_MODEL_IMPLEMENTATION::CPP_MODEL_IMPLEMENTATION(const ModuleProto &proto, InstanceInit &inst) : CPP_MODEL_INTERFACE(proto, inst), queueStore_(0) { } void CPP_MODEL_IMPLEMENTATION::Init() { incount.Initialize("incount",this); starsMonitor * m = monitor(); cts_ = ((int)InitialCTS.Value().value() == 0) ? false : true; queueSize_ = (int)MaximumQueueSize.Value().value(); ...

  28. How it fits in VCC (black.cpp) ... void CPP_MODEL_IMPLEMENTATION::Run() { if (CleartoSend.Enabled()) { incount++; if (incount.total() == 1000) incount.mgr()->runStars(); ... } void CPP_MODEL_IMPLEMENTATION::starsAbstraction() { QueueInput.count.setBound(25590); QueueOutput.count.setBound(QueueInput.count); incount.setBound(QueueInput.count/2+10); } ...

  29. S T A R S