Computational Models for Concurrent Streaming Applications

Transcription

1 2 Computational Models for Concurrent Streaming Applications The challenges of today Twan Basten Based on joint work with Marc Geilen, Sander Stuijk, and many others Department of Electrical Engineering Electronic Systems Knowing is not understanding. Charles Kettering 3 The problem: an example 4 Objectives Use-cases to be mapped onto a professional printer Copying (black&white, color, various paper sizes, zoom factors, ) Printing Scanning Simultaneous printing and scanning Reliable, resource-efficient embedded systems Fast, predictable design trajectories printer platform How many CPUs, GPUs? Processor speeds? How to achieve X images/min? Double resolution? Run-time changes in speed, job type, power budget?

2 5 Objectives 6 Objectives Reliable, resource-efficient embedded systems Fast, predictable design trajectories Reliable, resource-efficient embedded systems Fast, predictable design trajectories High-tech professional systems cell thales Systems-on-chip océ asml philips 5 nxp 7 Objectives 8 Trend: increasing complexity Reliable, resource-efficient embedded systems Fast, predictable design trajectories Multiprocessor systems / networking / concurrency Application convergence / application evolution Mixed data- and event processing Variability / dynamism Networked embedded systems Networked embedded systems 7 8

3 9 Scientific challenges 0 Outline Reliable, resource-efficient embedded systems Computational modeling and analysis Model-driven synthesis and run-time management Fast, predictable design trajectories Complexity reduction (Semi-)automatic system synthesis The challenges of today Computational models The dataflow hierarchy Kahn Process Networks Reactive Process Networks Analysis Looking forward An understanding of the natural world and what's in it is a source of not only a great curiosity but great fulfillment. David Attenborough 2 The essence: computational models on the interface between science and engineering Basic dimensions Aspects essential for predictability Metrics Computational models processing communication storage functionality concurrency timing energy quality functionality concurrency timing energy quality execution time energy dissipation perceived quality reconfiguration time energy

4 3 A model 4 Essential challenges predicts system metrics given parameter values predictability and efficiency are contradictory should be targeted to the problem at hand 5 6 Synchronous DataFlow ( [Lee 986]) The dataflow hierarchy rate token actor channel execution time A, B,2 C,2 : rates are fixed (weighted marked graphs from Petri-net theory) Homogeneous : all rates (marked graphs from Petri-net theory)

5 7 Synchronous DataFlow: actor firing ( [Lee 986]) rate token actor channel execution time A, B,2 C,2 2 : rates are fixed (weighted marked graphs from Petri-net theory) Homogeneous : all rates (marked graphs from Petri-net theory) 8 Dataflow expressiveness hierarchy and larger: Turing complete Better notions of expressiveness needed Unification needed : Reactive Process Networks : Kahn Process Networks DF: DataFlow : Dynamic DF : Scenario-Aware DF : Boolean DF : Cyclo-Static DF : Synchronous DF : Homogeneous 9 A gaming example 20 Application domain parameters / user interaction parameters / user interaction Reactive Process Networks () Automata / State machines mode change 3d video control mode change add/remove object renderers nrobj dynamic stream processing... scene graph & physics sg scene graphs object-based rendering fr frames filter & overlay streaming kernels Synchronous Data Flow () Kahn Process Networks ()

6 2 Kahn Process Networks ( [Kahn 974]) processes communicating via unbounded fifo queues Example 22 mixing() while(true){ read(in, frame); preprocess(frame); read(in2, frame2); Picture in Picture frame3 = combine(frame, frame2); write(out, frame3); } reads block on empty queues abstraction: only functionality, buffering processes: need to be functional writes may never block no global variables 23 : Denotational semantics 24 2 equivalent transformation processes = (mathematical) functions fifo queues = strings, sequences of data tokens if functions are continuous, then a network is also a continuous function G G Preserves actor firings, timing properties Does not preserve buffering aspects Algorithms operating directly on may be more efficient and/or provide better results (or they may not ) compositional semantics

7 25 2 equivalent transformation 26 Cyclo-Static DataFlow G Dataflow graph H.263 decoder ( [Bilsen et al 966]) sequence of rates sequence of execution times G G with 90 actors,, 3, 0,2 A,2,, B,,2 C,2,0,0 Allows the specification of certain iterations Can be transformed into an equivalent Algorithms operating directly on may be more efficient and/or provide better results The computational model selected in the NEST project 27 Boolean DataFlow 28 Scenario-Aware DataFlow ( [Buck 993]) the numbers of tokens produced or consumed in a firing can be a two-valued function of a control token for example: {T, F} switch {T, F} T F T F select ( [Theelen et al 2006]) H.263 Decoder Model Control channel Parameterized rate Detector... d d d VLD IDCT a Fixed rate c c b e FD MC RC 3 Kernel Data channel Allows the specification of conditions and iterations Cannot, in general, be transformed into an equivalent Turing-complete I P 99 P 99 P 0

8 29 Scenario-Aware DataFlow ( [Theelen et al 2006]) H.263 Decoder Model Control channel Parameterized rate Detector... d d d VLD IDCT a Fixed rate c c b e FD MC RC I P 99 P 99 P 0 3 Kernel Data channel x={30,40,50,60,70,80,99} Rate I P x P 0 a 0 0 b 0 x 0 c 99 x d 0 e 99 x 0 Execution time VLD P 0 0 others 40 IDCT P 0 0 others 7 I, P 0 0 P P MC P P P P P I 350 P 0 0 RC P 30, P 40, P P P 70, P 80, P FD All 0 30 : Fundamental limitation non-deterministic merge: forwards tokens selecting input arbitrarily outcomes: or or i.e., behavior is not a function! or 3 Dynamic DataFlow ( [Buck 993]) 32 the numbers of tokens produced or consumed in a firing may vary Kahn Process Networks

9 Example 33 mixing() while(true){ read(in, frame); preprocess(frame); read(in2, frame2); Picture in Picture frame3 = combine(frame, frame2); write(out, frame3); } 34 Denotational semantics processes = (mathematical) functions fifo queues = strings, sequences of data tokens if functions are continuous, then a network is also a continuous function reads block on empty queues writes may never block no global variables compositional semantics 35 Continuity 36 Kleene iteration monotonicity if input τ extends input σ then output f(τ) extends output f(σ) S: elementwise sum h 0 : prefix a 0 h : copy f(00)=0 f(000)= f g(00)= g 00 continuity bit-wise invert reverse output must be taken back!! generalization of monotonicity to inputs of arbitrary, particularly infinite, length continuity = streaming U i ε U = S(I,0U,00U) the continuous function of a network is the least fixpoint of a set of fixpoint equations and can be computed via a Kleene iteration U 0 = ε U i+ = S(I,0U i,00u i ) i = U(0) U() U(2) U(3) U(4) U(5) U(6) U(7) U(8) U(9)

10 37 Strengths & weaknesses 38 An operational view compositionality determinacy (execution order and timing) explicit concurrency explicit communication (via fifos; no shared variables) denotational semantics: what output is computed operational semantics: how the output is computed captures data-dependent streaming behavior high abstraction level needs run-time resource management when directly implemented cannot capture asynchronous reactive behavior undecidable, e.g., minimal buffer sizes strings are streams of tokens and fifo buffers of infinite capacity function as windows on those streams. an operational execution of functions conforms to (destructively) reading and writing tokens with internal computations in between. 39 Operational semantics 40 Operational semantics operational semantics captures all allowed ways to make behavior operational based on configurations i.e., + fifo fillings and transitions from one configuration to another one Configuration A transition Configuration B

11 4 The Kahn Principle 42 Implementations of s But hey, now we have two semantics of the model! Are they the same? bounded FIFOs combine aspects of data- and demand driven execution but how large should the FIFO buffers be? undecidable, FIFO sizes need to be managed at run-time The Kahn Principle: Any fair execution in the operational model realizes the denotational semantics, the mathematical function This provides the boundaries for realizations of s 43 A run-time environment (RTE) 44 requirements boundedness: fifo bounds may not grow indefinitely completeness: progress must be made on all outputs towards the output prescribed by the semantics Reactive Process Networks there exists an RTE satisfying these requirements prerequisites (undecidable in general!) boundedness: there exists a fair execution within finite fifo bounds effectiveness: every token that is produced is eventually also consumed [M.C.W. Geilen and T. Basten. Requirements on the Execution of Kahn Process Networks. Proc ESOP 2003.] [M.C.W. Geilen and T. Basten. Reactive Process Networks. Proc EMSOFT 2004.]

12 45 Application domain 46 A gaming example Reactive Process Networks () Automata / State machines Synchronous Data Flow () Kahn Process Networks () 47 Reactive Process Networks 48 Reactive Process Networks e automaton i o i i o o

13 49 Operational semantics 50 Operational semantics 5 Prioritizing events 52 Prototype implementation consumption of data allowed when events are present? theory: both options straightforward practice: choice prototype implementation of a programming environment for reconfigurations not affecting network structure events have priority over data?.5 input.5 output

14 53 Open issues 54 prototype implementation of arbitrary reconfigurations cases studies (programming styles, expressivity) timing reconfiguration/reaction times for events latency/throughput bounds on s as a whole efficient implementation of reconfiguration fifo sizes, deadlock analysis distribution analyzable subclasses (, ) Scenario-Aware DataFlow Analysis 55 Scenario-Aware DataFlow ( [Theelen et al 2006]) H.263 Decoder Model Control channel Parameterized rate Detector... d d d VLD IDCT a Fixed rate c c b e FD MC RC I P 99 P 99 P 0 3 Kernel Data channel x={30,40,50,60,70,80,99} Rate I P x P 0 a 0 0 b 0 x 0 c 99 x d 0 e 99 x 0 Execution time VLD P 0 0 others 40 IDCT P 0 0 others 7 I, P 0 0 P P MC P P P P P I 350 P 0 0 RC P 30, P 40, P P P 70, P 80, P FD All 0 56 A model-driven scenario-aware design flow extract application model keep trade-offs select operating point and switch dynamically

15 57 Synchronous DataFlow ( [Lee 986]) rate token actor channel execution time A, B,2 C,2 Throughput: average number of actor firings over time Iteration: smallest non-empty set of actor firings that does not change the token distribution (example: A:3, B:2, C:) 58 Throughput via state-space analysis Self-timed execution: Each actor fires as soon as it can fire Known to maximize throughput Execution state: distribution of tokens + remaining execution times Execution: transient + periodic phase A A Transient Phase Throughput can be calculated from the periodic phase A, C B A, C Periodic Phase B [Ghamarian et al 2006] Efficient implementation Consider one designated firing per iteration only to detect a recurrent state B A B 59 Throughput analysis results 60 Trade-off: storage vs. throughput State Space Traditional methods, all using conversion to Dasdan Gupta Howard Young Tarjan Orlin MP3 dec Modem Sample Rate >800 >800 >800 Satellite >800 >800 >800 H.263 decoder >800 >800 >800 Runtimes of various throughput analysis methods (in seconds) thro oughput multi-media applications ` DSP synthesis storage

16 6 Storage distribution 2 α 3 β 2 A, B,2 C,2 Tokens on channels must be stored in memory. Separate memory for each channel. Storage distribution, for example, α,β, 4,2 62 Problem definition through hput 2 α 3 β 2 A, B,2 C, ,2 5,3 6,3 6,2 7, distribution size Find all minimal storage distributions for any possible throughput 63 Dependency graph 64 Dependency graph 2 α 3 β 2 A, B,2 C,2 Storage distribution α, β 4,2 resolving storage dependencies may increase throughput firings in one period sp(β) tk(β) C 0 dependency: an actor firing start may depend on an actor firing end firings in one period sp(β) tk(β) C 0 dependency: an actor firing start may depend on an actor firing end B 0 sp(α) A 2 tk(α) B B 0 sp(α) A 2 tk(α) B sp - space tk - token tk(α) sp(α) A 3 A tk(a) 4 cycles denote storage dependencies sp - space tk - token tk(α) sp(α) A 3 A tk(a) 4 cycles denote storage dependencies

17 65 Abstract dependency graph dependencies between actors B 0 sp(α) A B C tk(α) tk(β) tk(a) sp(α) sp(β) tk(β) sp(β) C 0 A 2 tk(α) B sp(α) A 3 A tk(a) 4 abstract dependency graph contains all storage dependencies easily constructed from state-space exploration 66 Design-space exploration algorithm Given an graph G with storage distribution δ. Compute throughput and abstract dependency graph for G with δ 2. For each channel c with a storage dependency in Create new storage distribution by enlarging c 3. Repeat steps -2 All minimal storage distributions are found when starting from storage distribution 0,...,0 dependency graph may be very large tk(α) 67 Experimental results 68 Extensions Example Satellite MP3 H.263 #actors #channels Technique applies also to [Stuijk et al, IEEE T Comp 2008] Technique can be generalized to other types of resources [Yang et al, DATE 200] min throughput > 0 /7 0.8 /37 /2876 Distr. size Max throughput Approximation / /32 /0000 Distr. size increase 0buffers with 544 n times the minimal step size #Pareto points #Distributions Exec. time ms 7ms 2ms 53min

18 69 Scenario-aware performance analysis 70 3 toolkit [Geilen, ACM TECS 200] -based throughput analysis considers worst-case actor times Scenario-aware throughput analysis considers worst-case actor times per scenario, but it must consider scenario transitions Analyzing all scenario transitions separately can be avoided Separate scenario transitions with an invariant reference schedule 7 72 Challenges Looking Forward Suitable notions of expressivity Expressivity while maintaining analyzability and synthesizability Abstraction without loosing accuracy Composability and compositionality MoCs for non-functional aspects Unification of MoCs Multi-objective trade-off analysis Parametric analysis Model-driven design and synthesis flows Model-driven run-time systems

19 73 Thank you! Questions? More info: 3 toolkit: An understanding of the natural world and what's in it is a source of not only a great curiosity but great fulfillment. David Attenborough